Group Theoretical Methods in Physics

A guide to Lie superalgebras.- Supergravity in the physics of particles and fields.- Harmonic analysis on graded (or super) Lie groups.- The diagram lattice as structural principle in mathematics.- Kinematical symmetries in molecular quantum mechanics.- Symmetry of non-rigid molecules.- Some recent results on the metaplectic representation.- The nuclear collective model and the symplectic group.- Geometry of real and complex canonical transformations in quantum mechanics.- Composite particles and symplectic (SEMI-) groups.- Group theory of the Landau — Thermodynamic theory of continuous phase transitions in crystals.- Phase transitions, approach to equilibrium, and structural stability.- Topological classification of symmetry defects in ordered media.- Dynamical origin of symmetry.- Action of control semi groups on manifold and application to realization theory.- Some applications of the theory of semigroups to automata.- Position space renormalization group.- Static solitons in more than one dimension.- Remarks on the energy representation of Sobolev-Lie groups.- Unbounded representations of the Poincare and gauge groups in the indefinite metric quantization of the electromagnetic field.- On the construction of graded Lie algebras.- Exceptional parafermions in a Hilbert space over an associative algebra.- The SU(4) nuclear symmetry revisited.- The spinning electron.- Group theoretical expansions of scattering amplitudes for particles with spin.- On the extension of vector fields and the superluminal transformations.- A group theoretical derivation of the minimal coupling in elementary quantum mechanics.- Towards a constructive approach to supersymmetric ?.- The maximal Abelian subgroups of the conformal group of space-time.- The exceptional groups as candidates for supersymmetry.- Quark bag excitations, SL(3,R) spectrum generating group and vector states in e+e? annihilation.- Completeness of networks of states.- PUA representations of Shubnikov space groups and selection rules.- Computer programs for determining Wave Vector Selection Rules (WVSRs) for space groups.- Results of computer programs for determining the reductions of the Kronecker products of the irreducible representations of space groups.- Compatibility relations for factor systems and space group representations.- Bravais lattices associated with incommensurate crystal phases.- Ligand polarizations and lanthanide ion spectra.- Basic exchange integrals and the triple double coset symbol.- Group contractions and infrared effect in theories with spontaneous breakdown of symmetry.- Instantons in lattice models with discrete symmetries.- Spontaneous breakdown of symmetry and the generalized coherent states.- Molien function and calculation of invariant polynomials for space groups.- Gauge fields and quantum liquids.- A new model of a structural phase transition.- Application of Morse theory to the symmetry breaking in the Landau theory of second order phase transition.- Spontaneous breakdown of the gauge symmetry and observable phase operator.- Semigroups and effective structures of automata.- Studies of some physically-relevant representation groups.- Effective decompositions of automata.- On invariants and canonical forms for linear dynamical systems.- Mean ergodic semigroups of contractions in W*-algebras.- About some series associated to complex semi-simple Lie algebras.- Gelfand Lattice polynomials and finite irreducible representations of GL(n,¢)..- Partitions of integers and Lie algebras.- Lie elements, the killing form and trace identities.- Branching rule SO(7)?G2.- Simplified Racah's eingenval formula for the second order Casimir operator.- A note on the series expansions for the Racah coefficient.- Construction of O(3) shift operators and their use in classification of Lie algebras.- Wave functions of identical particles.- The metaplectic semigroup and the implementation of complex linear canonical transformations in quantum mechanics.- Weyl quantization and metaplectic representation.- On quantummechanical symmetry groups.- Non-bijective canonical transformations and their representations in quantum mechanics.- Kinematical symmetries of the nonlinear diffusion equations.- Lie pseudogroups and the structure of physical laws.- Equivalence of Kadison and Wigner symmetries in traditional quantum mechanics.- The coherent states associated with a compact semi-simple Lie group.- Theory of symmetry of infinite systems.- Group theoretic approach to similarity analysis with applications to the problems of wave propagation.- Generalized number operator in the Fock representation.- Quantization and deformation theroy.