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# Group theoretical methods in physics : proceedings of the XIIth International Colloquium, held at the International Centre for Theoretical Physics, Trieste, Italy, September 5-11, 1983 / edited by G. Denardo, G. Ghirardi, and T. Weber.

Material type: TextSeries: Lecture notes in physics ; 201.Publication details: 1984. Description: 1 online resource (xxvii, 518 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540388593; 3540388591Additional physical formats: Print version:: Group theoretical methods in physics.DDC classification: 530.1/5222 LOC classification: QC20.7.G76 | G78 1984Other classification: 31.21 | 31.30 | 33.06 | UD 8220 Online resources: Click here to access online
Contents:
The use and ultimate validity of invariance principles -- Cohomology and contraction: The "non-relativistic" limit revisited -- Linearization -- A unified approach -- Weyl kinematical groups of electromagnetic and energy-momentum tensors -- From spinors to probability amplitudes of external and internal variables for spinning particles -- A characterizatton of factor systems of locally-operating representations -- Recent developments on shift operators -- Unitary and non-unitary, multiplicity free irreducible representations of SL (3,R) -- The symmetry group of a differential equation -- Group contractions and the E(2)-like little group for massless particles as an infinite-momentum/zero-mass limit of the 0(3)-like little group for massive particles -- Representation approach to lattices of subgroups of space groups -- Young tableaux for the Lie superalgebra OSP(M/N) -- The associated Lie Algebra of $$\ddot x$$ + f2 $$\dot x$$ + f1x = f0 -- Three-dimensional commutative diagram of group homomorphisms -- Indecomposable representations of Verma type -- Some recent results on the SU(3)? SO(3) state labelling problem -- Irreducible projective representations of the generalized symmetric groups B n m -- Indecomposable representations of some graded Lie Algebras -- Stephen Paneitz: A brief appreciation -- Indecomposable representations of the Poincare group and associated fields -- SL(n, R)/SO(n) unirreps and group decontraction -- Hysteresis & universal bifurcation in natural processes -- Irreducible representations of the basic classical Lie superalgebras SU(m/n) ; SU(n/n)/U(1) ; OSp(m/2n) ; D(2/1 ;?) ; G(3) ; F(4). -- Group representations in indefinite metric spaces -- Tensor operator realisations of the classical Lie Algebras and non-trivial zeros of the 6j-symbol -- Yang -- Baxter algebras of dynamical charges in the chiral gross -- Neveu model -- Subgroups of Lie groups and symmetry reduction for nonlinear partial differential equations -- Spinorial description of Lie superalgebras -- Noetherian symmetries, backlund transformation and conservation laws for a completely integrable three dimensional system -- Einstein equations without killing vectors, self-dual Yang-Mills field and non-linear sigma models (integrability properties, links, new solutions) -- Jet bundle technique, Lie Bäcklund vector fields and diffusion equations -- A group-theoretic treatment of Gaussian optics and third-order aberrations -- Study of Michel's conjecture -- Conformally invariant solutions of Yang-Mills equations in Minkowski space -- Two body relativistic scattering with an 0(1,1) symmetric sqaure well potential -- Emergence of central extension of Kac-Moody algebra in quantum integrable models -- Cohomological interpretation of anomalies the example of the trace anomaly -- On pure, conformal and exotic spinors -- Pohlmeyer-type transformations in general relativity -- On group covariance and the law of motion in a generalized metric theory -- Minimalization of Higgs potentials with application to the SU(5) model -- Self-dual monopoles and calorons -- U(1) Invariant hierarchy theories in d-dimension antisymmetric gauge tensor fields -- Generalized connection forms with linearized curvature -- Dynamical symmetry breaking in S4 De Sitter space -- Applications of conformal invariance to gauge Quantum Field Theory -- On the necessity of breaking colour SUC(3) symmetry -- Massive vector superfields with SU(2) internal symmetry -- Supergravity in eleven-dimensional space-time -- Dimensional reduction of exceptional gauge groups and flavor chirality -- Seven -- Spheres from octonions -- A solution of Bianchi identities for extended supergravities -- N=2 unconstrained superfield supergravity from hypermultiplet -- Euclidean supersymmetries in three and four dimensions -- Gauge theories in higher dimensions: Linear relations for gauge fields, integrability conditions, spherical symmetry in eight dimensions -- Quantum vortices and diff (?3) -- The time dependent Sp(2,?) model for the breathing mode -- The quark structure of nuclei from a group theoretical viewpoint -- Group theoretic approach to spherical anharmonic oscillator -- Operator averages and orthogonalities -- Advances in the theory of collective motion in nuclei -- Quantum effects in classical phase space: Symplectic structures associated to the scattering of nuclear fragments -- Gamow states in momentum representation -- Geometry of nuclear collective motions -- Is it possible to separate the kinetic energy and the velocity field into a collective and an intrinsic part W.R.T. the GL+(3,)R) collectivity? -- Computer generated Clebsch-Gordan (C-G) coefficients for space groups -- Automorphism symmetries of space group representations -- Lattices of symmetric groups S5 and S6 and exomorphism of group-subgroup relations up to index 6 -- A direct-expansion method for tensor properties of crystals -- Isotropy groups of space groups -- A simple method for their determination -- Landau's theory of crystalline phase transitions in a superspace formulation -- Symmetry breaking in solid state and particle physics -- Counterexamples to the maximality conjecture of Landau-Higgs models -- Some mathematical problems in renormalization group theory -- On the Racah algebra for Shubnikov magnetic groups -- On periodic and non-periodic space fillings of Em obtained by projection -- Invariants for physically irreducible representations of space groups -- On symmetry aspects of phase transitions with coupled parameters -- Quasisymmetry (P-symmetry) in crystals -- Braid groups and Euclidean Lie algebras in statistical mechanics of spin systems -- Phase coexistence in many-fermion systems -- Mean field renormalization group approach to lattice models -- Linear-antilinear representations of magnetic line groups -- Anderson transition and nonlinear?-model -- Do energy bands in solids have an identity -- Coupling coefficients for the space group of the hexagonal close-packed structure -- Harmonic analysis on phase space and Born's metric for space time -- Generalized Chebyshev polynomials and characters of GL(N, C) and SL(N, C) (fragments of results) -- Tensor operators as an extension of the universal enveloping algebra -- A group-theoretical criterion for an Einstein-Podolsky-Rosen state -- Group theory algebras and bosonization -- SO(3) commutators for angular momentum and rotation observables -- Integrals of motion of nonstationary quantum systems -- Geometric properties of the lowest energy state for a polynomial Hamiltonian -- Groupes différentiels et physique mathématique -- Gauge invariance and canonical transformations in Dirac generalized mechanics.
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The use and ultimate validity of invariance principles -- Cohomology and contraction: The "non-relativistic" limit revisited -- Linearization -- A unified approach -- Weyl kinematical groups of electromagnetic and energy-momentum tensors -- From spinors to probability amplitudes of external and internal variables for spinning particles -- A characterizatton of factor systems of locally-operating representations -- Recent developments on shift operators -- Unitary and non-unitary, multiplicity free irreducible representations of SL (3,R) -- The symmetry group of a differential equation -- Group contractions and the E(2)-like little group for massless particles as an infinite-momentum/zero-mass limit of the 0(3)-like little group for massive particles -- Representation approach to lattices of subgroups of space groups -- Young tableaux for the Lie superalgebra OSP(M/N) -- The associated Lie Algebra of $$\ddot x$$ + f2 $$\dot x$$ + f1x = f0 -- Three-dimensional commutative diagram of group homomorphisms -- Indecomposable representations of Verma type -- Some recent results on the SU(3)? SO(3) state labelling problem -- Irreducible projective representations of the generalized symmetric groups B n m -- Indecomposable representations of some graded Lie Algebras -- Stephen Paneitz: A brief appreciation -- Indecomposable representations of the Poincare group and associated fields -- SL(n, R)/SO(n) unirreps and group decontraction -- Hysteresis & universal bifurcation in natural processes -- Irreducible representations of the basic classical Lie superalgebras SU(m/n) ; SU(n/n)/U(1) ; OSp(m/2n) ; D(2/1 ;?) ; G(3) ; F(4). -- Group representations in indefinite metric spaces -- Tensor operator realisations of the classical Lie Algebras and non-trivial zeros of the 6j-symbol -- Yang -- Baxter algebras of dynamical charges in the chiral gross -- Neveu model -- Subgroups of Lie groups and symmetry reduction for nonlinear partial differential equations -- Spinorial description of Lie superalgebras -- Noetherian symmetries, backlund transformation and conservation laws for a completely integrable three dimensional system -- Einstein equations without killing vectors, self-dual Yang-Mills field and non-linear sigma models (integrability properties, links, new solutions) -- Jet bundle technique, Lie Bäcklund vector fields and diffusion equations -- A group-theoretic treatment of Gaussian optics and third-order aberrations -- Study of Michel's conjecture -- Conformally invariant solutions of Yang-Mills equations in Minkowski space -- Two body relativistic scattering with an 0(1,1) symmetric sqaure well potential -- Emergence of central extension of Kac-Moody algebra in quantum integrable models -- Cohomological interpretation of anomalies the example of the trace anomaly -- On pure, conformal and exotic spinors -- Pohlmeyer-type transformations in general relativity -- On group covariance and the law of motion in a generalized metric theory -- Minimalization of Higgs potentials with application to the SU(5) model -- Self-dual monopoles and calorons -- U(1) Invariant hierarchy theories in d-dimension antisymmetric gauge tensor fields -- Generalized connection forms with linearized curvature -- Dynamical symmetry breaking in S4 De Sitter space -- Applications of conformal invariance to gauge Quantum Field Theory -- On the necessity of breaking colour SUC(3) symmetry -- Massive vector superfields with SU(2) internal symmetry -- Supergravity in eleven-dimensional space-time -- Dimensional reduction of exceptional gauge groups and flavor chirality -- Seven -- Spheres from octonions -- A solution of Bianchi identities for extended supergravities -- N=2 unconstrained superfield supergravity from hypermultiplet -- Euclidean supersymmetries in three and four dimensions -- Gauge theories in higher dimensions: Linear relations for gauge fields, integrability conditions, spherical symmetry in eight dimensions -- Quantum vortices and diff (?3) -- The time dependent Sp(2,?) model for the breathing mode -- The quark structure of nuclei from a group theoretical viewpoint -- Group theoretic approach to spherical anharmonic oscillator -- Operator averages and orthogonalities -- Advances in the theory of collective motion in nuclei -- Quantum effects in classical phase space: Symplectic structures associated to the scattering of nuclear fragments -- Gamow states in momentum representation -- Geometry of nuclear collective motions -- Is it possible to separate the kinetic energy and the velocity field into a collective and an intrinsic part W.R.T. the GL+(3,)R) collectivity? -- Computer generated Clebsch-Gordan (C-G) coefficients for space groups -- Automorphism symmetries of space group representations -- Lattices of symmetric groups S5 and S6 and exomorphism of group-subgroup relations up to index 6 -- A direct-expansion method for tensor properties of crystals -- Isotropy groups of space groups -- A simple method for their determination -- Landau's theory of crystalline phase transitions in a superspace formulation -- Symmetry breaking in solid state and particle physics -- Counterexamples to the maximality conjecture of Landau-Higgs models -- Some mathematical problems in renormalization group theory -- On the Racah algebra for Shubnikov magnetic groups -- On periodic and non-periodic space fillings of Em obtained by projection -- Invariants for physically irreducible representations of space groups -- On symmetry aspects of phase transitions with coupled parameters -- Quasisymmetry (P-symmetry) in crystals -- Braid groups and Euclidean Lie algebras in statistical mechanics of spin systems -- Phase coexistence in many-fermion systems -- Mean field renormalization group approach to lattice models -- Linear-antilinear representations of magnetic line groups -- Anderson transition and nonlinear?-model -- Do energy bands in solids have an identity -- Coupling coefficients for the space group of the hexagonal close-packed structure -- Harmonic analysis on phase space and Born's metric for space time -- Generalized Chebyshev polynomials and characters of GL(N, C) and SL(N, C) (fragments of results) -- Tensor operators as an extension of the universal enveloping algebra -- A group-theoretical criterion for an Einstein-Podolsky-Rosen state -- Group theory algebras and bosonization -- SO(3) commutators for angular momentum and rotation observables -- Integrals of motion of nonstationary quantum systems -- Geometric properties of the lowest energy state for a polynomial Hamiltonian -- Groupes différentiels et physique mathématique -- Gauge invariance and canonical transformations in Dirac generalized mechanics.

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