학술논문
Group theoretical methods in physics. Vol. 1--3.
Document Type
Proceedings Paper
Author
Source
Subject
22 Topological groups, Lie groups
22-06Proceedings, conferences, collections, etc.
22-06
Language
English
Abstract
Contents:\Volume 1. Part I. Group representations:\I. M. Gelʹfand, M. I. Graev and A. M. Vershik, The commutative model of the principal representation of the current group ${\rm SL}(2,{\bf R})^X$ with respect to a unipotent subgroup (pp. 3--22);A. M. Vershik, Infinite-dimensional metagonal and metaplectic groups (pp.\ 23--27);D. P. Zhelobenko, Reduction algebras and Gelʹfand-Zetlin bases (pp.\ 29--37);N. Ya. Vilenkin and L. M. Klyosova [L. M. Klesova], Functions of the discrete spectrum in harmonic analysis on hyperboloids (pp. 39--45);N. Ya. Vilenkin and A. P. Pavlyuk, Representations of some semisimple Lie groups and special functions of the matrix argument (pp. 47--54);R. L. Shapiro, On some realizations of the ${\rm IU}(n+1)$ group (pp.\ 55--59);A.-A. A. Jucys, Symmetric group representations and noncanonical bases in the subduction $U_{k(k+1)/2}\supset U_k$ (pp. 61--65);Yu. F. Smirnov, V. N. Tolstoy [V. N. Tolstoĭ], M. Havlíček, Č. Burdík and A. A. Sakharuk, The Dyson-type boson realizations for representations of the semisimple Lie algebras and superalgebras (pp.\ 67--76);V. N. Tolstoy [V. N. Tolstoĭ], Yu. F. Smirnov and Z. Pluhař, The Clebsch-Gordan coefficients of the ${\rm SU}(3)$ group and their symmetry properties (pp. 77--86);A. F. Nikiforov, S. K. Suslov and V. B. Uvarov, Classical orthogonal polynomials of a discrete variable in the theory of group representations (pp. 87--96);S. J. Ališauskas [Sigitas Ališauskas], Boundary value problems in the Wigner-Racah calculus of the compact Lie groups (pp. 97--102);E. Norvaišas, Clebsch-Gordan coefficients of the $\roman U_6$ group in the basis $\roman U_6\supset \roman U_3$ (pp. 103--106);V. P. Karassiov [V. P. Karasev], The Wigner-Racah algebras of ${\rm SU}(n)$ and polynomial bases of the representations ${\scr D}(\dot O_{n-1}J\dot O_{m-n-1})$ of ${\rm SU}(m)$ (pp. 107--114);I. V. Andreev, Invariant gluonic tensors of rank five (pp. 115--123);I. V. Andreev and B. O. Shpekpaev, Gluonic invariants (pp. 125--134).\parPart II. Coherent states:\R. J. Glauber, Quantum amplifiers, attenuators, and their irreversible behavior (pp. 137--148);Michael Martin Nieto, Coherent states with classical motion: from an analytic method complementary to group theory (pp. 149--166);I. V. Polubarinov, Phase space representations in quantum field theory (pp.\ 167--187);A. V. Gorokhov, Coherent states on Lie groups and path integrals (pp.\ 189--199);V. V. Dodonov, V. I. Manʹko and V. V. Semyonov [V. V. Semenov], The density matrix of canonically transformed Hamiltonians in the Fock basis (pp.\ 201--211);R. G. Agayeva [R. G. Agaeva], Calculation of collisionless current and thermoelectromotive force by the coherent-state method (pp. 213--222);S. G. Krivoshlykov, N. I. Petrov and I. N. Sissakian [I. N. Sisakyan], Coherent properties of optical fields in inhomogeneous media (pp. 223--230);V. V. Dodonov, V. I. Manʹko and S. M. Chumakov, The density matrix and excitation of a singular nonstationary oscillator at finite temperature (pp. 231--255).\parPart III. Symmetries in nuclear and atomic physics:\V. Vanagas, Symplectic models of the nucleus (pp. 259--282);R. M. Asherova, Yu. I. Nechaev and Yu. F. Smirnov, The application of the ${\rm Sp}(2,{\bf R})$ group in the deformed nuclei theory and in the scattering problem (pp. 283--292);V. G. Zelevinsky [V. G. Zelevinskiĭ], Collective excitations of spherical nuclei: group models and problems of microscopic justification (pp.\ 293--301);V. G. Zelevinsky [V. G. Zelevinskiĭ], A microscopic approach to the description of fluctuation and dissipation of nuclear collective motion (pp.\ 303--310);V. Č. Šimonis [V. Šimonis] and J. M. Kaniauskas [J. Kaniauskas], Dynamic symmetry ${\rm SO}(4,1)$ of the hydrogen atom in momentum space and generalized spherical functions (pp. 311--316);J. M. Kaniauskas [J. Kaniauskas], V. Č. Šimonis [V. Šimonis] and Z. B. Rudzikas, Group theoretical methods of investigation of approximate symmetries of complex atoms (pp. 317--324);I. M. Pavlichenkov, The Bargmann representation of the Lie groups in nuclear physics (pp. 325--330).\parPart IV. Symmetries of differential equations, their integrability, and the inverse scattering method:\D. R. Lebedev and A. O. Radul, Generalized internal long wave equations: construction, Hamiltonian structure, and conservation laws (pp. 333--351);V. K. Melʹnikov, Symmetries, nonlinear transformations, and equations integrable by the inverse scattering method (pp. 353--372);S. G. Gindikin, Manifolds of rational curves and nonlinear equations (pp.\ 373--383);B. S. Getmanov, Two-dimensional Lorentz-invariant field theory models with higher integrals of motion: complex scalar fields (pp. 385--397);A. N. Leznov and I. A. Fedoseev, Two-dimensional exactly integrable dynamical systems in the quantum region (pp. 399--406);V. G. Makhanʹkov and O. K. Pashaev, A new integrable model of QFT in the state space with indefinite metrics (pp. 407--414);B. G. Konopelʹchenko, Group-theoretical and Hamiltonian structures of the integrable nonlinear equations in $1+1$ and $2+1$ dimensions (pp.\ 415--428);V. A. Andreyev [V. A. Andreev], Bäcklund transformations of Painlevé equations (pp. 429--434);E. V. Doktorov, A sigma-model associated with the Ernst equation (pp.\ 435--442);A. N. Leznov, The internal symmetry group and methods of field theory for integrating exactly soluble dynamic systems (pp. 443--457);H. J. de Vega, The inverse scattering method and functional integrals (pp.\ 459--468);F. V. Kusmartsev and É. I. Rashba, Self-trapping from degenerate bands and plasma caviton formation: spontaneous symmetry breaking (pp. 469--475);L. M. Berkovič [L. M. Berkovich] and M. L. Nechaevsky [M. L.\ Nechaevskiĭ], On the group properties and integrability of the Fowler-Emden equations (pp. 477--488);W. I. Fushchich [V. I. Fushchich], N. I. Serov and W. M. Shtelen [V. M.\ Shtelenʹ], Some exact solutions of many-dimensional nonlinear d'Alembert, Liouville, eikonal, and Dirac equations (pp. 489--496);A. G. Nikitin, W. I. Fushchich [V. I. Fushchich] and V. A. Vladimirov, New symmetries and conservation laws for electromagnetic fields (pp. 497--505);G. A. Kotelʹnikov, Definition of group symmetry of differential equations (pp. 507--516);G. A. Kotelʹnikov, Invariance of the Schrödinger homogeneous equation relative to the Lie algebra of the conformal group ${\rm C}_{15}$ (pp.\ 517--520);G. A. Kotelʹnikov, Invariance of Maxwell homogeneous equations relative to the Galilei transformations (pp. 521--535);Yu. A. Danilov and G. I. Kuznetsov, Nonlinear equations and differential invariants (pp. 537--540).\parPart V. Stochastisation and nonintegrability:\S. M. Apenko, D. A. Kirzhnits and Yu. E. Lozovik, Dynamic chaos, Anderson localization, and confinement (pp. 543--546);S. G. Matinyan, G. K. Savvidy [G. K. Savvidi] and N. G.\ Ter-Arutunyan-Savvidy [N. G. Ter-Arutyunyan-Savvidi], Stochasticity of Yang-Mills classical mechanics and its elimination by the Higgs mechanism (pp. 547--552);Boris V. Chirikov [B. V. Chirikov], The nature and properties of dynamic chaos (pp. 553--564);E. S. Nicolaevsky [E. S. Nikolaevskiĭ] and L. N. Shchur, Symmetry of the Hamiltonian, intersection of separatrices, and nonintegrability of the Yang-Mills fields (pp. 565--573).\parPart VI. Generalities of quantum theory:\I. V. Polubarinov, Quantum mechanics and Hopf fiber bundles (pp. 577--589);V. V. Dodonov and V. I. Manʹko, Universal invariants of quantum systems and generalized uncertainty relations (pp. 591--612);M. B. Mensky [M. B. Menskiĭ], A group-theoretical approach to a path integral (pp. 613--630);Z. Perjés, Twistor internal symmetry groups (pp. 631--643);J.-P. Amiet and P. Huguenin, Wigner functions of unitary transformations (pp. 645--659);V. P. Karassiov [V. P. Karasev], The generating invariant formalism in many-body systems analysis (pp. 661--671);V. B. Serebrennikov and A. E. Shabad, Quantum-mechanical generators of groups of hidden broken symmetry and their classical limits (pp. 673--690);V. B. Serebrennikov and A. E. Shabad, Dynamic groups in problems with central dynamics (pp. 691--703);V. V. Dodonov and V. I. Manʹko, Wigner functions of a damped quantum oscillator (pp. 705--717).\parVolume 2. Part VII. Gravitation and cosmology:\M. A. Markov, Asymptotic freedom and entropy in a perpetually oscillating universe (pp. 3--9);V. A. Berezin, V. A. Kuzʹmin and I. I. Tkachev, Vacuum bubbles in the early Universe and general relativity (pp. 11--25);V. P. Frolov, The density matrix and generating functional for quantum processes in black holes (pp. 27--39);V. P. Frolov and A. I. Zelʹnikov, Vacuum polarization of massive fields near a rotating black hole (pp. 41--48);A. A. Bogush and V. S. Otchik, Representations of ${\rm SO}(4,1)$ and the Hawking effect in de Sitter space (pp. 49--58);U. Bleyer and H.-H. von Borzeszkowski, On gauge-invariant theories of gravitation (pp. 59--66);V. M. Nikolaenko, ${\rm U}(1)$ gauge model with a gravitational topological charge (pp. 67--71);A. V. Smilga, Spontaneous generation of the Newton constant in the renormalizable theory of gravity (pp. 73--77);V. I. Strazhev and P. L. Shkolʹnikov, Polarization symmetry of the gravitational field (pp. 79--85);J. Bičak, The symmetries of an asymptotically flat space-time and gravitational radiation (pp. 87--94);S. I. Babichenko and V. N. Rudenko, Restoration of external action on a gravitational antenna (pp. 95--111).\parPart VIII. Quantum field theory and elementary particles:\E. S. Fradkin and M. Ya. Palʹchik, New results in conformal invariant quantum field theory (pp. 115--133);A. Cabo and A. E. Shabad, Effective action for a nonabelian field with a nonvanishing source (pp. 135--152);A. Cabo and A. E. Shabad, Quantum theory of a gauge field with a nonvanishing external source. I. Canonical formalism and Furry picture (pp. 153--165);A. Cabo and A. E. Shabad, Quantum theory of a gauge field with a nonvanishing external source. II. Propagators and spectra in a nonabelian external field (pp. 167--185);I. A. Batalin and G. A. Vilkovisky [G. A. Vilkoviskiĭ], Closure of the gauge algebra, generalized Lie equations, and Feynman rules (pp. 187--205);D. M. Gitman and I. V. Tyutin, Canonical quantization of singular theories (pp. 207--237);A. O. Barvinsky [A. O. Barvinskiĭ], The double-dimensional regularization and gauge theories without ghosts (pp. 239--255);G. V. Grigoryan, R. P. Grigoryan and I. V. Tyutin, Symmetries of renormalized theories with symmetrical classical action (pp. 257--264);E. A. Tolkachev, Dual transformations in nonabelian gauge field theory (pp.\ 265--269);A. A. Bogush, A. M. Fedorovykh and L. F. Zhirkov, Some properties of local gauge transformation parameters in nonabelian field theory (pp. 271--277);A. S. Schwarz [A. S. Shvarts] and Yu. S. Tyupkin, Grand unification, strings, and mirror particles (pp. 279--289);G. M. Henkin [G. M. Khenkin], Yang-Mills-Higgs-Dirac fields and holomorphic vector bundles (pp. 291--302);M. A. Soloviev [M. A. Solovʹev], On the group of gauge transformations and Singer's theorem (pp. 303--308);V. N. Pervushin, On topological vacuum degeneracy in gauge theories (pp.\ 309--316);O. K. Kalashnikov, An asymptotically free ${\rm SU}(5)$ model of grand unification (pp. 317--371);M. V. Burova, O. K. Kalashnikov and V. B. Vologodsky [V. B.\ Vologodskiĭ], Mass hierarchy of scalar bosons in the ${\rm SU}(5)$ model (pp. 373--383);E. S. Fradkin and S. E. Konsteĭn [S. E. Konshteĭn], An asymptotically free ${\rm SU}(5)$ model of grand unification with four generations (pp. 385--411);A. Bohm [Arno Bohm], Hadronic rotational bands and constrained Hamiltonian mechanics of the quantum relativistic rotator (pp. 413--428);V. V. Khrushchov, On the properties of the scalar constituents of hadrons with respect to the ${\rm SU}(2)_{\rm L}\times {\rm U}(1)$ group (pp. 429--436);S. I. Kruglov and V. I. Strazhev, On the spacetime analog of the gauge theory with internal symmetry (pp. 437--442);A. Cabo and A. E. Shabad, The Lorentz-covariant formulation of temperature: Green's function method in relativistic statistics (pp. 443--458).\parVolume 3. Part IX. Supersymmetry, supergravity, and superalgebras:\Yu. I. Manin, Supersymmetry and supergravity in the superspace of null supergeodesics (pp. 461--468);B. Julia, Infinite-dimensional groups acting on (super)-gravity phase space (pp. 469--484);A. S. Galʹperin, V. I. Ogievetsky [V. I. Ogievetskiĭ] and E.\ Sokatchev, On a versatile model of supergravity (pp. 485--491);B. M. Zupnik, Unconstrained conformal superfields in $N=1$ supergravities with different off-mass structures (pp. 493--499);B. M. Zupnik, Extended conformal supergravity in chiral superspace (pp.\ 501--509);P. van Nieuwenhuizen, Supergravity on three-spheres (pp. 511--530);E. S. Fradkin and A. A. Tseytlin, Quantum properties of higher-dimensional and dimensionally reduced supersymmetric theories (pp. 531--544);G. V. Grigoryan, R. P. Grigoryan and I. V. Tyutin, Renormalization of the $N=4$ supergauge theory (pp. 545--557);K. S. Stelle, The finiteness of the $N=4$ supersymmetric Yang-Mills theory (pp. 559--571);M. I. Èĭdes, A. V. Smilga and M. I. Vysotsky [M. I. Vysotskiĭ], The massless gluino and pseudoscalar mesons (pp. 573--577);I. V. Volovich, Constraint equations in supersymmetric gauge theories and vector bundles over twistors (pp. 579--585);A. A. Rosly [A. A. Roslyĭ], Super Yang-Mills constraints as integrability conditions (pp. 587--593);E. A. Ivanov [Evgeniĭ Alekseevich Ivanov\asup{2}] and S. O. Krivonos, The ${\rm U}(1)$-supersymmetric extension of the Liouville equation (pp.\ 595--606);A. N. Leznov and V. V. Khrushchov, The supersymmetric Liouville equation in the quantum case (pp. 607--612);N. G. Pletnyov [N. G. Pletnëv] and V. V. Serebryakov, Superanalogies of constant-curvature space (pp. 613--622);B. L. Feĭgin and D. A. Leĭtes, New Lie superalgebras of string theories (pp. 623--629);B. L. Feĭgin, D. A. Leĭtes and V. V. Serganova, Kac-Moody superalgebras (pp. 631--637);V. V. Serganova, Outer automorphisms and real forms of Kac-Moody superalgebras (pp. 639--642);A. U. Klimyk and A. M. Gavrilik [O. M. Gavrilik], On the representations of noncompact global symmetry groups of the extended $N=6$ supergravity (pp.\ 643--648).\parPart X. Space groups and phase transitions:\O. V. Kovalev, Methods of irreducible corepresentations and induced representations in crystal physics (pp. 651--666);W. Sikora, Applications of the symmetry analysis method to structural and magnetic phase transitions in hexagonal manganites, ${\rm ErB}_4$ and ${\rm FeSiO}_4$ compounds (pp. 667--673);R. A. Èvarestov and V. P. Smirnov, Use of the space group factor decomposition in solid state theory (pp. 675--683);V. A. Koptsik, Color symmetry and scaling in phase transitions and critical phenomena theory (pp. 685--703);J. N. Kotzev, V. A. Koptsik and K. A. Rustamov, ``Chromomorphism'' of color groups and classification of phase transitions (pp. 705--713);V. A. Koptsik, I. L. Fedoseeva and Zh. N. M. Kuzhukeev, Eight-color space $P$-symmetry groups (programmed derivation) (pp. 715--723);J. L. Birman and A. I. Solomon, Dynamical groups and the coexistence of superconductivity, charge density waves, and magnetism (pp. 725--732);L. L. Boyle, Space group representations for crystal structure types (pp.\ 733--737);E. N. Ovchinnikova and R. N. Kuzʹmin, A group-theoretical approach to the analysis of the Mössbauer diffraction pattern (pp. 739--743);J. N. Kotzev and M. I. Aroyo, On the coupling coefficients for systems with anti\-unitary symmetry (pp. 745--752);A. G. Zhilich, A. A. Kiselev [A. Kiseliovas] and V. P. Smirnov, Space symmetry of orientationally disordered molecular crystals (pp. 753--762);L. Michel, The Landau theory of second-order phase transitions and the invariant theory (pp. 763--774);E. I. Kats and M. I. Monastyrsky [M. I. Monastyrskiĭ], Ordering in diskotic liquid crystals (pp. 775--786);Yu. A. Nepomnyashchy [Yu. A. Nepomnyashchiĭ], On the nature of the $\lambda$-transition parameter (pp. 787--793);V. I. Manʹko and D. A. Trifonov, Matrix elements of finite transformations of Lie groups in the bases of coherent and Fock states (pp.\ 795--810);V. I. Manʹko, Integrals of motion and the symmetry of quantum systems (pp. 811--825).\par \{The papers of mathematical interest that appear to be in final form are being reviewed individually.\}\