The XI International Conference on Symmetry Methods in
Physics (SYMPHYS-11) was held in Prague, the Czech Republic, from 21 to 24
June 2004. It was organized by the Bogoliubov Laboratory of Theoretical
Physics, the Doppler Institute, and the Czech Technical University
(Prague) in the framework of the Blokhintsev-Votruba programme. A total of
about 100 scientists from all over the world took part in the conference.
The conference series was initiated by Professor Yakov A. Smorodinsky (1917-1992), an outstanding theoretical physicist. Professor Smorodinsky organized the first five conferences that were held at the Institute of Physics and Power Engineering in Obninsk from 1986 to 1991. The next three conferences of the series were held at the Joint Institute for Nuclear Research in Dubna in 1993, 1995 and 1997, while the last two took place at the Yerevan State University (Armenia) in 2001 and 2003. The SYMPHYS-11 conference is devoted to general studies and applications of group theoretical methods in modern physics. It covers fields of research where symmetry-based methods play an important role. The programme included the following topics: symmetries of fundamental interactions; Lie groups, supergroups and nonlinear algebraic structures; symmetries of difference and differential equations; nonlinear systems and quantum chaos; quantum optics and coherent states; periodic and aperiodic structures. ## BPS domain wall in massive nonlinear sigma model in harmonic superspaceMasato Arai, Jiri NiederleInstitute of
Physics, AS CR, 182 21, Prague 8, Czech RepublicEvgeny
IvanovBogoliubov Laboratory of Theoretical Physics, JINR,
Dubna, 141 980 Moscow region, RussiaBPS wall solutions in four-dimensional massive N = 2
nonlinear sigma models are studied in the off-shell harmonic superspace
approach in which N = 2 supersymmetry is manifest. The general nonlinear
sigma model can be described by an analytic harmonic potential which is
the hyper-Kahler analog of the Kahler potential in N = 1 theory. We
examine the massive nonlinear sigma model with multi-center
four-dimensional target hyper-Kahler metrics and derive the corresponding
BPS equation. We study in some detail two particular cases with the
Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two
separate limits, both Taub-NUT and Eguchi-Hanson metrics. We find that
domain wall solutions exist only in the double Taub-NUT case including its
Eguchi-Hanson limit. PACS:
11.10.-z;11.27.+d;11.30.PbKeywords: domain wall, supersymmetry,
harmonic superspaceFile size: 201
KB## Anomalies and superpotential in N = 1 noncommutative gauge theoriesF. Ardalan and N. SadooghiDepartment of
Physics, Sharif University of Technology P.O. Box 11365-9161, Tehran, Iran
and Institute for Studies in Theoretical Physics and Mathematics (IPM)
P.O. Box 19395-5531, Tehran, Iran The anomaly of various currents in the noncommutative
supersymmetric N = 1, U(1) gauge theory are calculated and the effective
superpotential obtained. PACS: 11.15.Bt
Keywords: noncommutative N = 1 supersymmety, effective
superpotential File size: 111
KB## Generalized dimensional reduction of D = 6 (2,0) chiral supergravityL. Andrianopoli, S. FerraraCERN, Theory
Division, CH 1211 Geneva 23, SwitzerlandM.A.
LledoDepartamento de Fisica Teorica, Universidad de Valencia
and IFIC, C/Dr. Moliner, 50, E-46100 Burjassot (Valencia),
Spain.We report on the Scherk-Schwarz reduction of D = 6 (2,0)
supergravity coupled to matter and its interpretation as D = 5 gauged N =
2 supergravity of no-scale type. PACS: 04.65.+e,
04.50.+h, 11.10.KkKeywords: Scherk-Schwarz , 6D supergravity,
dimensional reductionFile size: 124
KB## Algebraic construction of integrable and super integrable hierarchiesH. AratynDepartment of Physics,
University of Illinois at Chicago 845 W. Taylor St., Chicago, Illinois,
60607-7059J.F. Gomes and A.H. ZimermanInstituto de
Fisica Teorica - IFT/UNESP Rua Pamplona 145, 01405-900, S~ao Paulo - SP,
BrazilA general construction of integrable hierarchies based on
afine Lie algebras is presented. The models are specified according to
some algebraic data and their time evolution is obtained from solutions of
the zero curvature condition. Such framework provides an unified treatment
of relativistic and non relativistic models. The extension to the
construction of supersymmetric integrable hierarchies is proposed. An
explicit example of N = 2 super mKdV and sinh-Gordon is
presented. PACS: 11.25.Hf, 02.30.IkKeywords:
integrability, supersymmetric integrable modelsFile size: 141
KB## On sl(N) and sl(M|N) integrable open spin chainsD. Arnaudon, N.
Crampe, A. Doikou, L. Frappat, E. RagoucyLaboratoire
d'Annecy-le-Vieux de Physique Theorique LAPTH CNRS, UMR 5108, associee a
l'Universite de Savoie LAPP, BP 110, F - 74941 Annecy-le-Vieux Cedex,
FranceJ. AvanLaboratoire de Physique Theorique et
Modelisation Universite de Cergy, 5 mail Gay-Lussac, Neuville-sur-Oise F -
95031 Cergy-Pontoise Cedex, FranceWe study open spin chains based on rational sl(N) and
sl(M|N) R-matrices. We classify the solutions of the re ection equations,
for both the soliton-preserving and soliton- non-preserving cases. We then
write the Bethe equations for these open spin
chains. PACS: 02.20.Uw, 03.65.Fd,
75.10.PqKeywords: spin chains, Yangians, quantum groups,
Yang-Baxter equationFile size: 154
KB## Non-generic symmetries and surface termsDumitru
BaleanuDepartment of Mathematics and Computer Sciences, Faculty
of Arts and Sciences, University of Cankaya, Ankara 06530, Turkey
andInstitute of Space Sciences, P.O.BOX, MG-23, R 76900, Magurele-Bucharest, Romania Integrable geometries were obtained by adding a total
time derivative involving the components of the angular momentum to a
given free Lagrangian. The motion on a sphere and its induced geometries
are examined in details. PACS:
02.40.-ky.Keywords: Killing-Yano tensors, non-generic
symmetries, surface termsFile size: 77
KB## The covering problem related to quasicrystalsLubomira Balkova,
Zuzana MasakovaDepartment of Mathematics, Faculty of Nuclear
Sciences and Physical Engineering, Czech Technical University, Trojanova
13, 120 00 Praha 2, Czech RepublicWe study mathematical models of quasicrystalline
materials/non-crystallographic solids with long range aperiodic order. A
natural generalization of crystallographic lattices are the so-called
Meyer sets. They are uniformly discrete, relatively dense point sets with
the property of almost lattices. This property ensures that there is only
a finite number of local configurations of atoms in the model of the
material. The most commonly studied class of Meyer sets arises in the well
known cut-and-project scheme. For cut-and-project sets with compact
acceptance window we study a finite set of the Meyer property. This task
can be transformed into the problem of covering of the difference set by
open copies. The cardinality fof the minimal covering is called the Meyer
number. We show that f is bounded on the space of convex compact sets. We
give estimates on the universal upper bound of the Meyer number of
dimension 2 and 3. We determine the values of f for some special types of
dimension 2. We further show that f is not bounded if we relax the
condition of convexity. PACS: 61.44.Br, 02.40.Ft,
02.40.-kKeywords: quasicrystals, cut-and-project sets, Meyer
sets, covering problemFile size: 153
KB## Special theory of relativity and conventionalityV.S. BarashenkovLaboratory of
Information Technologies, Joint Institute of Nuclear Research, 141980
Dubna, RussiaE.Kapuscik and D. WcisloDepartment of
Physics, University of Lodz, ul. Pomorska 149/153, PL 90236 Lodz,
PolandDepartment of Theoretical Astrophysics, H.Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, ul. Eliasza-Radzikowskiego 152, PL 31342 Krakow, Poland The general properties of the clock synchronization in
Special Theory of Relativity with different "one way" velocities of light
are discussed. It is argued that the customary irreducible element of
conventionality of the synchronization problem may be
eliminated. PACS: 03.30.+pKeywords: special
theory of relativity, conventionalityFile size: 74
KB## Little group kinematics associated with classical opticsS. BaskalDepartment of Physics, Middle East
Technical University, 06531 Ankara, TurkeyY.S.
KimDepartment of Physics, University of Maryland, College Park,
Maryland 20742, U.S.A.Little groups are the subgroups of the Poincare group
whose transformations leave the four-momentum of a relativistic particle
invariant. Massless particle representations can be obtained from their
massive counterparts through a contraction procedure. The two by two
matrix representations of little groups as well as of other kinematical
effects of special relativity, like Wigner rotations are observed to
coincide with the matrix formulations of some interesting classical ray
optics phenomena. Examples include beam cycles in laser cavities, image
focusing in a one-lens-camera, multilens optics and interferometers. Thus,
it is argued that optical implementations can be exploited as analogue
processors for special relativity. PACS: 11.30.Cp,
42.79.BhKeywords: Wigner's little groups, classical
opticsFile size: 108 KB## Nonlinear algebraic structuresN. Belalouiy, L.
Khodjaz and H. BennacerLPMPS, Departement de Physique, Faculte
des Sciences, Universite Mentouri Constantine, Constantine,
AlgeriaWe paraquantize the bosonic (resp. the Neuveu Shwarz
spinning) string theory. Unlike the Ardalan and Mansouri work, the
paraquantum system is so that both the center of mass variables and the
excitation modes of the string verify paracommutation relations. We find
existence possibilities of parabosonic (resp. paraspinning) strings
defined in a noncommutative space-time at space-time dimensions other than
D = 26 (resp. D = 10). We investigate then the existence possibilities of
the. D = 3, 4, 6 parasuperstring. The two cases, parabose-parafermi (resp.
bose-parafermi) superstrings are considered. In the first one, the
spectrum is discussed through the partition functions for D = 3, 4, 6.
Despite of the parastatistical algebraic structure of the dynamical
variables, the combined set of the generators of the symmetries forms the
algebra of the Super Symmetric Quantum Mechanic (resp. the ParaSSQM in the
sense of Beckers and Debergh). PACS: 11.30.Cp ,
11.25.HfKeywords: parastring, Poincar parasuperalgebra,
critical dimentions, noncommutativityFile size: 157
KB## Chaining spins from (super)Yang-MillsS. Bellucci,
P.Y. Casteill, J.F. Morales, C. SochichiuLaboratori Nazionali
di Frascati, Via E. Fermi 40, 00044 Frascati, ItalyWe review the spin bit model describing anomalous
dimensions of the operators of Super Yang-Mills theory. We concentrate
here on the scalar sector. In the limit of large N this model coincides
with integrable spin chain while at finite N it has nontrivial chain
splitting and joining interaction. File size: 108
KB## 2k-dimensional N = 8 supersymmetric quantum mechanicsS. BellucciINFN-Laboratori Nazionali di
Frascati, C.P. 13, 00044 Frascati, ItalyS. Krivonos, A.
ShcherbakovBogoliubov Laboratory of Theoretical Physics, JINR,
141980 Dubna, RussiaA. NersessianYerevan State
University and Yerevan Physics Institute, Yerevan, Armenia, Artsakh State
University, Stepanakert, Nagorny Karabakh, ArmeniaWe demonstrate that two-dimensional N = 8 supersymmetric
quantum mechanics which inherits the most interesting properties of N = 2;
d = 4 SYM can be constructed if the reduction to one dimension is
performed in terms of the basic object - N = 2; d = 4 vector multiplet. In
such a reduction only complex scalar fields from the N = 2; d = 4 vector
multiplet become physical bosons in d = 1, while the rest of the bosonic
components are reduced to auxiliary fields thus giving rise to (2, 8, 6)
supermultiplet in d = 1. We construct the most general action for this
supermultiplet with all possible FI terms included and explicitly
demonstrate that the action possesses duality symmetry extended to the
fermionic sector of theory. To deal with the second-class constraints
presented in the system, we introduce the Dirac brackets for the canonical
variables and find supercharges and Hamiltonian which form the N = 8 super
Poincare algebra with central charges. Finally, we explicitly present the
generalization of the two-dimensional N = 8 SQM to the 2k-dimensional case
with a special Kahler geometry in the target
space. PACS: 11.25.Hf, 11.30.PbKeywords:
supersymmetry, quantum mechanics, special Kahler geometryFile
size: 158 KB## The representation theory of the Heisenberg group and beyondAlastair BrodlieSchool of Mathematics,
University of LeedsIn this paper we present some recent and new developments
in the theory of p- mechanics. p-Mechanics is a consistent physical theory
which contains both classical and quantum mechanics. The Heisenberg group
and its representation theory is the basis of p-mechanics. We give a
summary of recent results on p-mechanical observables, states and
canonical transformations. In doing so we exhibit relations between the
quantum and classical image of these objects. We also present some new
work on the Kepler/Coulomb problem. This involves constructing a new
Hilbert space which represents the dynamics of the Kepler/Coulomb problem
in a simple form. PACS: 03.65.Ca,
03.65.Db.Keywords: Heisenberg group, quantum mechanics,
coherent states, p-mechanics, canonical transformations, Kepler/Coulomb
problemFile size: 184 KB## Algebraic solutions for Schrödinger equations with time-varying potentials and time-dependent boundary conditionsB.L. BurrowsStaffordshire University
Stafford UKM. CohenThe Hebrew University Jerusalem
IsraelLie algebraic methods, which have been used widely for
stationary states of quantum mechanical systems are extended here to treat
time–dependent problems. Difficulties may arise at points where the
potential is discontinuous or has discontinuous derivatives and from
certain imposed boundary conditions. The simplicity and elegance of the
usual algebraic methods can be retained for such problems by redefining
the domain of the operators using techniques developed by Lighthill to
introduce generalized functions. We treat a model double–well subject to
time–varying external fields as well as problems with time–dependent
boundary conditions. PACS: 81.R.15Keywords:
algebraic solutions, time–dependentFile size: 104
KB## Exact plasma equilibria from symmetries and transformations of MHD and CGL equilibrium equationsAlexei F.
CheviakovDepartment of Mathematics, Queen's University at
Kingston, ON, Canada K7L 3N6Exact isotropic and anisotropic plasma equilibria are
constructed as solutions to nonlinear 3D Magnetohydrodynamic (MHD) and
anisotropic Chew-Goldberger-Low (CGL) plasma equilibrium equations, using
the representation of equilibrium equations in coordinates connected with
magnetic surfaces. Infinite-dimensional symmetries of MHD and CGL
equilibrium equations used in this construction are discussed from the
prospective of Lie group analysis. The infinite-parameter set of
transformations between MHD and CGL equilibrium systems is employed to
produce families of anisotropic (CGL) equilibria from particular isotropic
(MHD) ones. Solutions produced with the presented method are generally
fully 3D solutions with no geometrical symmetries; they have different
topologies and physical properties, and can serve as models of
astrophysical phenomena. PACS: 52.30.Cv, 05.45.-a,
02.30.Jr, 02.90.+p.Keywords: MHD, plasma equilibria, Lie group
of symmetries, exact solutionsFile size: 333
KB## Stationary axially symmetric gravitation fields in Einstein theoryE. Chubaryan and H. AbazyanDepartment of
Physics, Yerevan State University 1 Alex Manoogian St., 375049 Yerevan,
ArmeniaIn many recent astrophysical applications of the theory
of dense matter it is necessary to investigate the properties of rapidly
rotating compact objects within general relativity theory. The reason of
this development is the hope that changes in the internal structure of the
dense matter, e.g. during phase transitions, could have observable
consequences for the dynamics of the rotational behavior of these objects.
Particular examples are the observations of glitches and postglitch
relaxation in pulsars, which are discussed as signals for superfluidity in
nuclear matter and the suggestion that the braking index is remarkably
enhanced when a quark matter core occurs in the center of a pulsar during
its spin–down evolution. Further constraints for the nuclear equation of
state come from the observation of quasi–periodic brightness oscillations
(QPO’s) in low–mass–X–ray binaries, which entail mass and radius limits
for rapidly rotating neutron stars. File size: 191
KB## On the self-similarities of the rhombic Penrose tilingsNicolae
CotfasFaculty of Physics, University of Bucharest PO Box 76 -
54, Postal Office 76, Bucharest, RomaniaWe prove that the original Penrose tilings of the plane
admit an infinite number of independent scaling factors and an infinite
number of in ation centers. Our results are based on the definition of
these tilings in terms of strip projection method proposed by Katz and
Duneau shortly after the discovery of
quasicrystals. PACS: 61.44.BrKeywords:
Penrose tiling, self-similarity, scaling factor, in ation center,
quasicrystalFile size: 96 KB## Extension of Moyal-deformed hierarchies of soliton equationsAristophanes DimakisDepartment of
Financial and Management Engineering University of the Aegean, 31 Fostini
Str., GR–82100 Chios, GreeceFolkert
Müller-HoissenMax-Planck-Institut für Strömungsforschung
Bunsenstrasse 10, D–37073 Göttingen, GermanyMoyal–deformed hierarchies of soliton equations can be
extended to larger hierarchies by including additional evolution equations
with respect to the deformation parameters. A general framework is
presented in which the extension is universally determined and which
applies to several deformed hierarchies, including the noncommutative KP,
modified KP, and Toda lattice hierarchy. We prove a Birkhoff factorization
relation for the extended ncKP and ncmKP hierarchies. Also reductions of
the latter hierarchies are briefly discussed. Furthermore, some results
concerning the extended ncKP hierarchy are recalled from previous
work. PACS: 02.30.Ik,05.45.YvKeywords:
deformation, factorization, hierarchy, KP, Moyal, soliton, star–product,
Toda latticeFile size: 286 KB## Characters of D = 4 conformal supersymmetryV.K.
DobrevInstitute of Nuclear Research and Nuclear Energy,
Bulgarian Academy of Sciences 72 Tsarigradsko Chaussee, 1784 Sofia,
BulgariaWe give character formulae for the positive energy
unitary irreducible representations of the N-extended D = 4 conformal
superalgebras su(2; 2=N). Using these we also derive decompositions of
long superfields as they descend to the unitarity threshold. These results
are also applicable to irreps of the complex Lie superalgebras
sl(4=N). PACS: 11.30.Pb,11.25.HfKeywords:
supersymmetry, conformal, charactersFile size: 211
KB## Non-Hermitian Hamiltonians and supersymmetric quantum mechanicsQuentin Duret and Francois GieresInstitut
de Physique Nucleaire de Lyon, Universite Lyon 1, Bat. Paul Dirac 4 rue
Enrico Fermi, F-69622 Villeurbanne CedexWe review non-Hermitian Hamiltonians following
Mostafazadeh, while expanding on the underlying mathematical details. To
conclude, we shortly summarize pseudo-supersymmetric quantum
mechanics. PACS: 03.65.Ca, 03.65.FdKeywords:
Non-Hermitian operators with real spectrum, PT-symmetry, supersymmetric
quantum mechanicsFile size: 210
KB## Solutions of the Camassa-Holm hierarchy in 2+1 dimensionsP.G. EstevezArea de Fisica Teorica.
Universidad de Salamanca, Salamanca 37008, SpainJ.
PradaDepartamento de Matematicas. Universidad de Salamanca,
Salamanca 37008, SpainWe consider solutions of a generalization of the
Camassa-Holm hierarchy to (2+1) dimensions that include, in particular,
the well-known multipeakons solutions for the celebrated Camassa-Holm
equation. PACS: 02.30.Jr, 02.30.IkKeywords:
Camassa-Holm, peakons, shallow-waterFile size: 116
KB## On supersymmetric Q-ballsAndrzej M.
FrydryszakInstitute of Theoretical Physics, University of
Wroclaw, pl. M. Borna 9, 50-204 Wroclaw, PolandMichael A.
KnyazevDepartment of Informative Technologies and
Robototechnics, Belarussian National Technical University, Scarina Av. 65,
220013 Minsk, BelarusWe present some facts related to the charged
nontopological solutions of nonlinear field equations known as Q-balls.
Using simplified field equations from the bosonic sector of the
supersymmetric model we discuss an approximate solution with the spherical
symmetry. PACS: 11.30.Pb, 05.45.YuKeywords:
solitons, supersymmetry, nontopological solutionsFile size: 108
KB## Space groups for aperiodic crystalsJean-Pierre
Gazeau and Avi ElkharratLaboratoire de Physique Theorique de la
Matiere Condensee, Boite 7020, Universite Paris 7-Denis Diderot, 75251
Paris Cedex 05Christiane FrougnyLaboratoire
d'Informatique Algorithmique: Fondements et Applications, UMR 7089 CNRS,
Boite 7014, Universite Paris 7-Denis Diderot, 75251 Paris Cedex 05, and
Universite Paris 8Jean-Louis Verger-GaugryInstitut
Fourier, UMR 5582 CNRS, Universite Grenoble I, BP 74, 38402 Saint-Martin
d'HeresWe report on the existence of symmetry plane-groups for
quasiperiodic point-sets named beta-lattices. Like lattices are vector
superpositions of integers, beta-lattices are vector superpositions of
beta-integers. When beta > 1 is a quadratic Pisot-Vijayaraghavan (PV)
algebraic unit, the set of beta-integers can be equipped with an abelian
group structure and an internal multiplicative law. When beta is equal to
special values, we show that these arithmetic and algebraic structures
lead to freely generated symmetry plane- groups for beta-lattices. These
plane-groups are based on repetitions of discrete adapted rotations and
translations we shall refer to as beta-rotations and beta-translations.
Hence beta-lattices, endowed with beta-rotations and beta-translations,
can be viewed like lattices. We also show that, at large distances,
beta-lattices and their symmetries behave asymptotically like lattices and
lattice symmetries respectively. PACS:
02.20.-a,61.44.-nKeywords: beta-lattices, Pisot numbers,
quasicrystals, tilings, plane groupsFile size: 278
KB## Surfaces in su(N) algebra via sigma models on Minkowski spaceA.M. GrundlandCentre de Recherches
Mathematiques, Universite de Montreal C. P. 6128, Succ. Centre-ville,
Montreal, (QC) H3C 3J7, Canada, Universite du Quebec, Trois-Rivieres CP500
(QC) G9A 5H7, CanadaL. SnoblCentre de Recherches
Mathematiques, Universite de Montreal C. P. 6128, Succ. Centre-ville,
Montreal, (QC) H3C 3J7, Canada, Faculty of Nuclear Sciences and Physical
Engineering, Czech Technical University Brehova 7, 115 19 Prague 1, Czech
RepublicWe review our recent results concerning two-dimensional
smooth orientable surfaces immersed in su(N) Lie algebras. These are
derived from the sigma model defined on Minkowski space. The structural
equations of such surfaces expressed in terms of any regular solution of
the model are found. This is carried out using a moving frame adapted to
the surface. A procedure for construction of such surfaces is proposed and
illustrated by several examples obtained from the model in dim =
1. PACS: 02.40.Hw, 02.20.QsKeywords: sigma
models, structural equations of surfaces, integrable systems, Lie
algebrasFile size: 340 KB## Quantum (anti)de Sitter algebras and generalizations of the kappa-Minkowski spaceFrancisco J. Herranz, Angel
BallesterosDepartamento de Fisica, Universidad de Burgos Avda.
Cantabria s.n., 09006 Burgos, SpainN. Rossano
BrunoDipartimento di Fisica, Universita di Roma Tre and INFN
Sez. Roma Tre Via Vasca Navale 84, 00146 Roma, ItalyWe present two different quantum deformations for the
(anti)de Sitter algebras and groups. The former is a non-standard
(triangular) deformation of SO(4; 2) realized as the conformal group of
the (3+1)D Minkowskian spacetime, while the latter is a standard
(quasitriangular) deformation of both SO(2; 2) and SO(3; 1) expressed as
the kinematical groups of the (2+1)D anti-de Sitter and de Sitter
spacetimes, respectively. The Hopf structure of the quantum algebra and a
study of the dual quantum group are presented for each deformation. These
results enable us to propose new non-commutative spacetimes that can be
interpreted as generalizations of the kappa-Minkowski space, either by
considering a variable deformation parameter (depending on the boost
coordinates) in the conformal deformation, or by introducing an explicit
curvature/cosmological constant in the kinematical one; kappa-Minkowski
turns out to be the common first-order structure for all of these quantum
spaces. Some properties provided by these deformations, such as dimensions
of the deformation parameter (related with the Planck length), space
isotropy, deformed boost transformations, etc., are also
commented. PACS: 02.20.Uw, 11.30.-j,
04.60.-mKeywords: quantum algebras, deformation, Minkowski,
anti-de Sitter, Poincare, noncommutative spacetimeFile size:
176 KB## Quasi-exact solvability of the Dirac equationsChoon-Lin HoDepartment of Physics, Tamkang
University, Tamsui 25137, Taiwan, R.O.C.We present a general procedure for determining
quasi–exact solvability of the Dirac and the Pauli equation with an
underlying sl(2) symmetry. This procedure makes full use of the close
connection between quasi–exactly solvable systems and
supersymmetry. PACS: 03.65.-w,
03.65.PmKeywords: quasi–exact solvability, Dirac
equationsFile size: 113 KB## A product formula and combinatorial field theoryA. Horzela, P.
BlasiakH. Niewodniczanski Institute of Nuclear Physics, Polish
Academy of Sciences, ul. Eliasza-Radzikowskiego 152, PL 31342 Krakow,
PolandLaboratoire de Physique Theorique des Liquides, Universite Pierre et Marie Curie, Tour 24 - 2e et., 4 Pl.Jussieu, F 75252 Paris Cedex 05, France G. E. H. DuchampUniversite de Rouen,
LIFAR, F 76821 Mont-Saint Aignan Cedex, FranceK. A. Penson and
A. I. SolomonLaboratoire de Physique Theorique des Liquides,
Universite Pierre et Marie Curie, Tour 24 - 2e et., 4 Pl.Jussieu, F 75252
Paris Cedex 05, FranceThe Open University, Physics and Astronomy Department, Milton Keynes MK7 6AA, United Kingdom We treat the problem of normally ordering expressions
involving the standard boson operators a, a+ where [a, a+] = 1. We show
that a simple product formula for formal power series - essentially an
extension of the Taylor expansion - leads to a double exponential formula
which enables a powerful graphical description of the generating functions
of the combinatorial sequences associated with such functions - in
essence, a combinatorial field theory. We apply these techniques to some
examples related to specific physical
Hamiltonians. PACS: 03.65.Fd,
05.30.Jp,Keywords: boson normal ordering,
combinatoricsFile size: 422 KB## Symmetries and graded contractions of the Pauli graded sl(3, C)Jiri Hrivnak, Petr NovotnyDepartment of Physics,
Faculty of Nuclear sciences and Physical Engineering, Czech Technical
University, Brehova 7, 115 19 Prague 1, Czech RepublicPresented results were achieved in collaboration with
Miloslav Havlicek, Jiri Patera and Jiri Tolar. We consider the Pauli
grading of the Lie algebra sl(3, C) and use a concept of graded
contractions to construct non-isomorphic Lie algebras of dimension 8,
while preserving the Pauli grading. We show how the symmetry group of a
grading simplifies the solution of contraction equations and
identification of results. We give examples of resulting Lie algebras.
Complete results will be published elsewhere. PACS:
02.20.SvKeywords: Lie algebra, gradingFile size: 172
KB## Recoupling theory of many-body quantum theoryWilliam P. JoyceDepartment of Physics and
Astronomy, University of Canterbury Private Bag 4800, New
ZealandIn this paper we sketch the foundations of recoupling
theory. Introduction of an indistinguishability principle leads to Pauli
Exclusion and confinement. We discuss its application to SU(3)
colour. PACS: 02.10.Ws 12.38.AwKeywords:
recoupling, monoidal category, Pauli exclusion confinement,
quarksFile size: 138 KB## On a group-theoretical approach to the periodic table of chemical elementsMaurice R. KiblerInstitut de Physique
Nucleaire de Lyon, IN2P3-CNRS et Universite Claude Bernard 43 Bd du 11
Novembre 1918, F-69622 Villeurbanne Cedex, FranceThis paper is concerned with the application of the group
SO(4; 2) SU(2) to the periodic table of chemical elements. It is shown how
the Madelung rule of the atomic shell model can be used for setting up a
periodic table that can be further rationalized via the group SO(4; 2)
SU(2) and some of its subgroups. Qualitative results are obtained from the
table and the general lines of a programme for a quantitative approach to
the properties of chemical elements are developed on the basis of the
group SO(4; 2) SU(2). PACS: 03.65.Fd,
31.15.HzKeywords: hydrogen-like atom, harmonic oscillator,
invariance and non-invariance groups, Lie algebra under constraints,
Madelung rule, periodic tableFile size: 300
KB## Quantum entanglement and dynamical symmetriesAlexander A. Klyachko and Alexander S.
ShumovskyFaculty of Science, Bilkent University, Bilkent,
Ankara, 06800, TurkeyDefinition of maximum entanglement in terms of a novel
variational principle for quantum uctuations and its corollaries are
discussed. PACS: 03.65.Ud, 03.67.MnKeywords:
entanglement, quantum fluctuations, quantum measurementsFile
size: 133 KB## SU(1,1) algebra and interacting families of Calogero particlesMarijan MilekovicPhysics Department,
Faculty of Science, Bijenicka c. 32, 10002 Zagreb,
CroatiaStjepan Meljanac, Andjelo Samsarov, Marko
StojicRudjer Boskovic Institute, Bijenicka c. 54, 10002 Zagreb,
CroatiaA one-dimensional model with interacting families of
Calogero-type particles is studied. It includes harmonic, two-body and
three-body interactions among particles. We find the exact eigenenergies
corresponding to a class of the exact eigenstates of the model. We
emphasize the universal SU(1; 1) structure of the model. We show how SU(1;
1) generators for the whole system are composed of SU(1; 1) generators of
arbitrary subsystems. By imposing the conditions for the absence of the
three-body interaction, we find certain relations between the coupling
constants. PACS: 03.65.Fd; 03.65.SqKeywords:
multispecies Calogero model, SU(1; 1) symmetry, interacting
familiesFile size: 117 KB## Newton-Wigner postulates and commutativity of position operatorsR.M. Mir-KasimovBogoliubov Laboratory of
Theoretical Physics, Joint Institute for Nuclear Research 141980, Dubna,
Russia andDepartment of Mathematics, Izmir Institute of Tehnology 35430, Urla/Izmir, Turkey Commutativity of the position operator components is one
of the Newton-Wigner postulates for the localized states tacitly included
in the list. Omitting it gives additional possibilities to use the
Poincare group representations for the analysis of the concept of the
relativistic quantum localized states. PACS: 02.20.Uw,
02.20.-aKeywords: localization, noncommutative,
relativisticFile size: 160 KB## Method of categorical extension of Cayley-Klein groupsS.S. MoskaliukBogolyubov Institute for
Theoretical Physics, 14b Metrolohichna st., Kyiv, UkraineThe method of categorical extension of the Cayley-Klein
groups is developed. The method uses the Cayley-Klein spaces, as objects
of the Cayley-Klein category, endowed with all possible linear relations
or bilinear forms as morphisms. PACS:
02.20.QsKeywords: group theory, category theoryFile
size: 140 KB## Non-trivial extension of the Poincare algebra for antisymmetric gauge fieldsG. MoultakaLaboratoire de
Physique Mathematique et Theorique, CNRS UMR 5825, Universite Montpellier
II, Place E. Bataillon, 34095 Montpellier, FranceM. Rausch de
Traubenberg and A. TanasakLaboratoire de Physique Theorique,
CNRS UMR 7085, Universite Louis Pasteur 3 rue de l'Universite, 67084
Strasbourg, FranceWe investigate a non-trivial extension of the
D-dimensional Poincare algebra. Matrix representations are obtained. The
bosonic multiplets contain antisymmetric tensor fields. It turns out that
this symmetry acts in a natural geometric way on these p-forms. Some field
theoretical aspects of this symmetry are studied and invariant Lagrangians
are explicitly given. PACS: 03.50.Kk,
03.65.Fd,11.10.Kk,11.30.LyKeywords: algebraic methods,
extension of the Poincare algebra, p-forms, field theoryFile
size: 159 KB## On conservation laws for the potential Zabolotskaya-Khokhlov equationV. RosenhausDepartment of Mathematics and
Statistics, California State University, Chico, CA 95929, USAWe study local conservation laws for the potential
Zabolotskaya-Khokhlov equation in three-dimensional case. We analyze an
infinite Lie point symmetry group of the equation, and generate a finite
number of conserved quantities corresponding to infinite symmetries
through appropriate boundary conditions. PACS:
11.30.-j, 02.20.TwKeywords: infinite symmetries, conservation
lawsFile size: 104 KB## Some features about toric quaternionic Kahler geometry in D = 4O.P. SantillanBogoliubov Laboratory of Theoretical
Physics, JINR 141 980 Dubna, Moscow Reg., RussiaA.G.
ZorinFaculty of Physics, MSU, Vorobjovy Gory, Moscow, 119899,
RussiaWe explain some features about toric self dual structures
and toric quaternionic Kahler manifolds in four dimensions. Applications
are outlined. Keywords: Toda equation, Einstein-Weyl
structuresFile size: 100 KB## Lorentz-like formulation of Galilean field theoriesEsdras SantosDepartment of Physics,
University of Alberta, Edmonton, Alberta, Canada, T6G 2J1Faqir
KhannaDepartment of Physics, University of Alberta, Edmonton,
Alberta, Canada, T6G 2J1, TRIUMF, 4004, Wesbrook Mall, Vancouver, British
Columbia, Canada, V6T 2A3Marc de MontignyFaculte
Saint-Jean, University of Alberta, Edmonton, Alberta, Canada, T6C
4G9Department of Physics, University of Alberta, Edmonton, Alberta, Canada, T6G 2J1 We construct non-relativistic Lagrangian field models by
enforcing Galilean covariance with a (4; 1) Minkowski manifold followed by
a projection onto the (3; 1) Newtonian space- time. We discuss scalar,
Fermi and gauge fields, as well as interactions between some of these
fields. The Galilean covariant formalism provides an elegant construction
of the Lagrangians which describe the electric and magnetic limits of
Galilean electromagnetism. As further examples of scalar fields, we
discuss various models of fluids and super fluids. Then, we turn to linear
wave equations, and consider the Dirac Lagrangian which allows one to
retrieve the Levy-Leblond wave equations. We examine the situation where
the Fermi field interacts with an abelian gauge field. Finally, we study
the Bhabha equations for spins 0 and 1. PACS: 03.50.De;
03.65.Pm; 47.10.+gKeywords: Galilean invariance, wave
equations, electromagnetismFile size: 159
KB## Saturation and non-linear effects in diffractive processesO.V. Selyugin and J.R. CudellInstitut de
Physique, Bat. B5a, Universite de Liege 4000 Liege, BelgiqueThrough a direct implementation of the saturation regime
resulting from the unitarity limit in the impact parameter representation,
we explore various possibilities for the energy dependence of hadronic
scattering. We show that it is possible to obtain a good description of
the scattering amplitude from a hard pomeron provided one includes
non-linear effects PACS: 62.20Keywords:
diffraction, unitarity, non-linear equations, total cross
sectionsFile size: 151 KB## The evolution of solutions of plane ideal plasticityS.I.
SenashovSiberian State Aero-Cosmic University, Krasnoyarsk,
660014 RussiaA. YakhnoCUCEI, Universidad de
Guadalajara, Guadalajara, MexicoIt's well known, that the symmetries of a system of
differential equations allow transforming its solutions to solutions of
this system. Using this property, from two known solutions of the theory
of plasticity: the solution of Nadai for circular cavity stressed by
normal and shear pressure, and Prandtl's solution for a block compressed
between perfectly rough plates, there were constructed new analytical
exact solutions of the system of two-dimensional ideal plasticity
equations. PACS: 46.35+z; 02.20-aKeywords:
plasticity, symmetry analysis, Lie group and algebra methods, exact
solutions of differential equationsFile size: 93
KB## Partition functions and graphs: A combinatorial approachA. I. SolomonThe Open University, Physics
and Astronomy Department Milton Keynes MK7 6AA, United
KingdomLaboratoire de Physique Theorique des Liquides, Universite Pierre et Marie Curie Tour 24 - 2e et., 4 Pl.Jussieu, F 75252 Paris Cedex 05, France P. BlasiakH.Niewodniczanski Institute of
Nuclear Physics, Polish Academy of Sciences ul. Eliasza-Radzikowskiego
152, PL 31342 Krakow, PolandLaboratoire de Physique Theorique des Liquides, Universite Pierre et Marie Curie Tour 24 - 2e et., 4 Pl.Jussieu, F 75252 Paris Cedex 05, France G. E. H.
Duchamp,Universite de Rouen, LIFAR, F 76821 Mont-Saint Aignan
Cedex, FranceA. HorzelaH.Niewodniczanski Institute
of Nuclear Physics, Polish Academy of Sciences ul. Eliasza-Radzikowskiego
152, PL 31342 Krakow, PolandK. A. PensonLaboratoire
de Physique Theorique des Liquides, Universite Pierre & Marie Curie
Tour 24 - 2e et., 4 Pl.Jussieu, F 75252 Paris Cedex 05, FranceAlthough symmetry methods and analysis are a necessary
ingredient in every physicist's toolkit, rather less use has been made of
combinatorial methods. One exception is in the realm of Statistical
Physics, where the calculation of the partition function, for example, is
essentially a combinatorial problem. In this talk we shall show that one
approach is via the normal ordering of the second quantized operators
appearing in the partition function. This in turn leads to a combinatorial
graphical description, giving essentially Feynman-type graphs associated
with the theory. We illustrate this methodology by the explicit
calculation of two model examples, the free boson gas and a super uid
boson model. We show how the calculation of partition functions can be
facilitated by knowledge of the combinatorics of the boson normal ordering
problem; this naturally gives rise to the Bell numbers of combinatorics.
The associated graphical representation of these numbers gives a
perturbation expansion in terms of a sequence of graphs analogous to
zero-dimensional Feynman diagrams. PACS: 03.65.Fd,
05.30.Jp,Keywords: boson normal ordering,
combinatoricsFile size: 211 KB## On systems of diffusion equationsC.
SophocleousDepartment of Mathematics and Statistics, University
of Cyprus, CY 1678 Nicosia, CyprusR.J. WiltshireThe
Division of Mathematics and Statistics, The University of Glamorgan,
Pontypridd CF37 1DL, Great BritainWe consider systems of diffusion equations that have
considerable interest in Soil Science and Mathematical Biology. We
construct non-local symmetries, known as potential symmetries. Furthermore
we present linearizing mappings. PACS: 02.30.Jr;
02.20.TwKeywords: diffusion equations, potential symmetries,
linearizing mappingsFile size: 126
KB## Deformed solitons: The case of two coupled scalar fieldsA. de Souza DutraUNESP-Campus de
Guaratinguet´a-DFQ, Av. Dr. Ariberto Pereira da Cunha, 333 C.P. 205,
12516-410 Guaratinguet´a SP BrasilIn this work, we present a general procedure, which is
able to generate new exact solitonic models in 1+1 dimensions, from a
known one, consisting of two coupled scalar fields. An interesting
consequence of the method, is that of the appearing of nontrivial
extensions, where the deformed systems presents other BPS solitons than
that appearing in the original model. Finally we take a particular
example, in order to check the above mentioned
features. PACS: 11.27.+d, 11.30.ErKeywords:
solitons, deformationsFile size: 108
KB## A division algebra classification of generalized supersymmetriesFrancesco ToppanCBPF, CCP, Rua Dr.
Xavier Sigaud 150, cep 22290–180, Rio de Janeiro, BrazilGeneralized supersymmetries admitting bosonic tensorial
central charges are classi- fied in accordance with their division algebra
properties. Division algebra consistent constraints lead (in the complex
and quaternionic cases) to the classes of hermitian and holomorphic
generalized supersymmetries. Applications to the analytic continuation of
the M–algebra to the Euclidean and the systematic investigation of certain
classes of models in generic space–times are briefly
mentioned. PACS: 11.30.PbKeywords:
supersymmetry, M–theoryFile size: 225
KB## Finiteness of generalized Chern-Simons thoeriesD.K.VolinInstitute for Theoretical and
Experimental Physics, 117259, Moscow, RussiaInstitute for Theoretical Physics, 03143, Kyiv, Ukraine and Physics Department, T.Shevchenko Kyiv State University, 01003, Kyiv, Ukraine We study the perturbation theory for the example of a
topological Batalin-Vilkovisky theory and show that it is free from the UV
divergences. In fact, the property of finiteness can be generalized for
some class of theories, which we describe here. 3-dimensional Chern-Simons
and 2-dimensional topological Yang-Mills theories belong to this
class. PACS: 00.00.xyKeywords: BV formalism,
topological theory, Chern-Simons, BFFile size: 98
KB## Similarity solutions of an equation describing ice sheet dynamicsR.J. WiltshireThe Division of Mathematics
and Statistics, The University of Glamorgan Pontypridd CF37 1DL, Great
BritainThis paper focus's upon the derivation of the similarity
solutions of a free boundary problem arising in glaciology. With reference
to shallow ice sheet ow we present a potential symmetry analysis of the
second order non-linear degenerate parabolic equation that describe
non-Newtonian ice sheet dynamics in the isothermal case. A full classical
and also a non-classical symmetry analysis is presented. A particular
example of a similarity solution to a problem formulated with Cauchy
boundary conditions is described. This demonstrates the existence of a
free moving boundary and also an accumulation-ablation function with
realistic physical properties. PACS:
02.30.Jr,02.30.Gp,83.10.Bb,47.50+dKeywords: non-linear
degenerate equations, ice ow dynamics, potential symmetriesFile
size: 142 KB## Space-group approach to the wavefunction of a Cooper pair. Application to unconventional superconductorsV.G.
YarzhemskyInstitute of General and Inorganic Chemistry of
RASZero-total momentum two-electron wavefunction in crystal
space-groups are constructed making use of induced representation method
and projection operator technique. Theory is applied to analysis of nodal
structure of Cooper pairs in unconventional supercondectors. Theoretical
results are compared with experimental data. PACS:
03.65.Fd,74.70.Tx,74.72.-hKeywords: Space groups,
superconducting order parameter, strongly correlated electronic systems,
unconventional superconductorsFile size: 154
KB## PT-symmetry, ghosts, supersymmetry and Klein-Gordon equationMiloslav ZnojilNuclear Physics Institute,
250 68 Rez, Czech RepublicParallels between the concepts of symmetry, supersymmetry
and (recently introduced) PT -symmetry are reviewed and discussed, with
particular emphasis on the new insight in quantum mechanics which is
rendered possible by their combined use. PACS:
03.65.GeKeywords: supersymmetric quantum mechanics, parity
times time reversal symmetry, non-Hermitian Hamiltonians with real
spectra, pseudo-metrics in Hilbert space, factorization method,
Klein-Gordon equationFile size: 122
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