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 (Q1078679)

The volume of Lecture Notes in Physics under review presents itself the proceedings of the XII International Colloquium on Group Theoretical Methods in Physics which was hold at the International Centre for Theoretical Physics in Trieste, in 5-11 September, 1983. This proceedings cover all fields of theoretical physics in which the group-theoretical methods are applied, and taking this fact into accont, they are partitioned into the following seven sections: 1. Group representations, group extensions, and contractions and bifurcations. 2. Completely integrable systems. 3. Elementary particles and gauge theories. 4. Supersymmetry and supergravity. 5. Atomic and nuclear physics. 6. Symmetries in condensed matter physics and statistical mechanics. 7. Canonical transformations and quantum mechanics. These proceedings are opened by the special contribution 'The use and ultimate validity of invariance principles' due to \textit{E. P. Wigner}. The first section consists among others of the following contributions: 'Linearization - a unified approach' by \textit{R. L. Anderson} and \textit{E. Taflin}, 'The symmetry group of a differential equation' by \textit{M. Hamermesh}, 'Some recent results on the SU(3)\(\supset SO(3)\) state labelling problem' by \textit{C. Quesne}, 'Group representations in indefinite metric space' by \textit{P. M. van den Broek}, and the others. The next section involves particularly the following reports: 'A group- theoretical treatment of Gaussian optics and third-order aberrations' by \textit{K. B. Wolf}, 'Yang-Baxter algebras of dynamical charges in the chiral Gross-Neveu model' by \textit{H. Eichenherr}, 'Subgroups of Lie groups and symmetry reduction for nonlinear partial differential equations' by \textit{A. M. Grundland}, \textit{J. Harnad}, and \textit{P. Winternitz}, etc. The Wolf's paper is based on the following idea: optical systems produce canonical transformations on the phase space of position and direction of light rays. In his report \textit{A. R. Chowdhury} made the analysis of importance of the Noetherian transformation laws for three-dimensional completely integrable nonlinear systems, and obtained, in particular, the new form of the Bäcklund transformation for the three-dimensional Kadomtsev-Petviashvili equation. \textit{W.-H. Steeb} and \textit{W. Strampp} studied the existence of the Lie-Bäcklund vector fields for various types of diffusion equations. The following reports contribute to section 3: 'On the necessity of breaking colour \(SU_ C(3)\) symmetry' by \textit{J. Werle}, 'Applications of conformal invariance to gauge quantum field theory' by \textit{I. T. Todorov}, 'Self-dual monopoles and calorons' by \textit{W. Nahm}, 'Generalized connection forms with linearized curvature' by \textit{F. B. Pasemann}, 'Dynamical symmetry breaking in \(S^ 4\) De Sitter space' by \textit{E. Spallucci}, and the others. In the contributions to the next section the following questions are discussed: supergravity in eleven- dimensional space-time (\textit{F. Englert} and \textit{H. Nicolai}), the Euclidean supersymmetry in three and four dimensions (\textit{A. Nowicki}), gauge theories in dimensions higher than four (\textit{J. Nuyts}), dynamics of quantum vortices in superfluids (\textit{M. Rasetti} and \textit{T. Regge}), etc. Section 5 is devoted to discussing such problems: \textit{P. Van Leuven} and his coworkers demonstrated the great importance of the Sp(2, \({\mathbb{R}})\) group for study of the nature of the nuclear breathing mode, or giant monopole excitation; \textit{K. Bleuler} studied the quark structure of spherical nuclei based on the group-theoretical approach; \textit{B. Ghosh} and \textit{R. K. Roychoudhury} presented the O(2,1) group-theoretical approach to study the problem of spherical anharmonic oscillator; \textit{B. R. Judd} discussed the problems of operator averages and orthogonalities; \textit{P. Kramer} analyzed the dynamical implication of invariance of the collective nuclear Hamiltonian relative to SO(n, \({\mathbb{R}})\); \textit{M. Moshinsky} discussed the connection between the collective behavior of many-body systems and several symplectic geometry concepts. Section 6 involves the following contributions: 'Automorphism symmetries of space group representations' by \textit{R. Dirl}, 'Landau's theory of crystalline phase transitions in a superspace formulation' by \textit{A. Janner}, \textit{T. Janssen}, and \textit{J. C. Toledano}, 'Symmetry breaking in solid state and particle physics' and 'Counterexamples to the maximality conjecture of Landau-Higgs models' by \textit{M. V. Jarić}, 'On periodic and non-periodic space fillings of \({\mathbb{E}}^ m\) obtained by projection' by \textit{P. Kramer} and \textit{R. Neri}, 'Phase coexistence in many-fermion systems' by \textit{A. I. Solomon} and \textit{J. L. Birman}, 'Do energy bands in solids have an identity?' by \textit{J. Zak}, 'Anderson transition and nonlinear \(\sigma\)-model' by \textit{F. Wegner}, etc. The abstracts of the papers, contributed to the last section, are: \textit{S. T. Ali} gives the analysis of the specific representation of the Poincaré group on phase space which is associated with the stochastic phase space approach; \textit{H. Bacry} defines the generalized Chebyshev polynomials and their relation with characters of GL(n, \({\mathbb{C}})\) and SL(n, \({\mathbb{C}})\); a global, coordinate-free algebraic formulation of the SU(3) tensor operator structure, which involves the universal enveloping algebra of SU(3), is presented by \textit{L. C. Biedenharn} and \textit{D. E. Flath}. \textit{F. Herbut} and \textit{M. Vujičić} derive the group- theoretical criterion for the Eistein-Podolsky-Rosen state. The method of bosonization of algebras and its diverse physical implications are discussed by \textit{A. J. Kálnay} and \textit{R. A. Tello-Llanos}. \textit{J. Krause} uses SU(3) commutators for angular momentum and rotation observables. \textit{V. I. Man'ko} presents the review on quantum integrals of motion of non-stationary systems with n degrees of freedom. \textit{W. Schweizer} and \textit{P. Kramer} examine the geometric properties of the lowest energy state for the class of polynomial Hamiltonians which are at most quadratic in the basis of the Lie algebra SU(2), or SU(1,1), and etc.