## Group theoretical methods in physics: proceedings of the third Yurmala seminar, Yurmala, USSR 22-24 May 1985These Proceedings cover various topics in modern physics in which group theoretical methods can be applied effectively. The two volumes, containing over 100 papers, cover such areas as representation theory, the theory and applications of dynamical symmetries and coherent states, symmetries in atomic, molecular, nuclear and elementary particle physics, field theory including gauge theories, supersymmetry and supergravity, general relativity and cosmology, the theory of space groups and its applications to solid state physics and phase transitions, the problems of quantum and classical mechanics and paraxial optics, and the theory of nonlinear equations and solitons. |

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### Contents

Twenty years of dynamical groups and spectrum generating algebras | 3 |

Quantum invariants and state system generating algebra | 51 |

Transvector algebras in representation theory and dynamic symmetry | 71 |

Copyright | |

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2-gauge aberration angular momentum arbitrary atomic axes axis boson calculate canonical basis Casimir operators classical Clebsch-Gordan coefficients coefficients commutation components consider construct corresponding crystal defined denote described determined dimensional dynamic symmetry eigenvalues energy expansion expression finite formula G-pattern Galilei gauge field gauge group gauge theories group G group-theoretical Hamiltonian highest weight interaction invariant irreducible representations irrep isomorphic lattice Lett Lie algebra Lie groups linear linking coefficient magnetic Math matrix elements Maxwell equations modules Moscow Russian multiplets multiplicity Nauka nonlinear Nucl nuclei obtained octonions optical oscillator p-symmetry parameters particle permutation phase Phys polynomials Preprint problem properties quantum numbers quantum system reduced relations relativistic rotation satisfy scalar solution space groups spectrum spin string structure SU(N subalgebra subgroup subspace symmetry group tensor Theorem tion transformations transition unitary variables vector wave Weyl Wigner