## Group Theoretical Methods in Physics: Proceedings of the Third Yurmala Seminar, Yurmala, Ussr, 22-24 May 1985, Volume 1Moiseĭ Aleksandrovich Markov, Vladimir Ivanovich Mano, Victor V. Dodonov These 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

Harmonic superspace and extended supersymmetries | 47 |

B Zupnik | 61 |

Spontaneous compactification of extra space dimensions in supergravities with | 79 |

Stochastic quantization supersymmetry and renormalization | 97 |

Integrals of motion in supersymmetric quantum mechanics | 113 |

Arrangements of real hyperplanes and Zamolodchikov equations | 151 |

Background field method in covariant secondquantized string theory | 167 |

String model of hadrons and their interactions | 183 |

Hidden symmetry of selfdual equations for static axialsymmetric gauge fields | 427 |

Absolute invariants and Kortewegde Vries equation | 449 |

Some exact solutions of fivedimensional nonlinear wave equation | 469 |

Zeros of polynomials and generalized Chebyshev polynomials | 481 |

Irreducible representations of SO n SO p q SU n S4 and their matrix elements | 495 |

Representation of the rotation group and discrete orthogonal polynomials | 513 |

SL 2 R overlap coefficients between SO 2 and SO 1 1 subgroup reductions | 531 |

Lorentz group and some integral representations for Bessel functions | 551 |

Symmetry breaking for rotating closed relativistic string and Regge trajectorys | 197 |

The interaction hierarchy stability in GUT models | 213 |

Spectral asymmetry and the QCD chiral Lagrangian | 227 |

Towards nonperturbative calculating hadronic field correlators | 241 |

Embeddings of OSP N2 and the associated nonlinear supersymmetric equations | 255 |

Integrable models of field theory and simple Lie algebras and superalgebras | 299 |

Supersymmetric generalized Toda lattice | 315 |

The GelfandTseitlin basis for the Lie superalgebra gl nlm | 337 |

Solitons as purely algebraic construction | 357 |

Nijenhuis operators in classical dynamics | 385 |

Multidimensional nonlinear dynamical systems | 413 |

Perturbation theory at large order | 573 |

Path integrals on compact Kahler manifolds | 595 |

On relativistic and nonrelativistic Coulomb problems for a particle of arbitrary spin | 609 |

Singlevaluedness of wave functions and scattering in multiply connected spaces | 625 |

An algebraic approach to coupled oscillators | 643 |

Normal forms of threedimensional relaxation dynamical systems | 657 |

One extract solution of the relativistic twobody problem in the Poincare approach | 673 |

Toroid moments as general physical parameters | 683 |

Closed analytic expressions for some useful sums and integrals involving Legendre | 699 |

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