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Advances in the Mathematical Sciences
Topics in Statistical and Theoretical Physics
Edited by: R. L. Dobrushin and R. A. Minlos, Institute for Information Transmission Problems, Moscow, Russia, M. A. Shubin, Northeastern University, Boston, MA, and A. M. Vershik, Russian Academy of Sciences, St. Petersburg, Russia

American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
1996; 223 pp; hardcover
Volume: 177
ISBN-10: 0-8218-0425-1
ISBN-13: 978-0-8218-0425-4
List Price: US$126
Member Price: US$100.80
Order Code: TRANS2/177
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This is the second of two volumes dedicated to the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization and Grassmannian analysis ("supermathematics").

Collected here are papers by many of his colleagues and others who worked in related areas, representing a wide spectrum of topics in statistical and theoretical physics and allied areas of mathematics. In particular, several papers discuss various aspects of quantum field theory and related questions of supersymmetry, geometry, and representation theory. Other papers are devoted to problems of quasi-classical approximation and mathematical models of statistical physics.


Graduate students and research mathematicians specializing in mathematical problems related to quantum field theory and statistical physics, including related problems of geometry, differential equations, and representation theory.

Table of Contents

  • D. Bar-Moshe and M. S. Marinov -- Berezin quantization and unitary representations of Lie groups
  • I. A. Batalin and I. V. Tyutin -- Generalized field-antifield formalism
  • A. M. Budylin and V. S. Buslaev -- Semiclassical integral equations on the semiaxis
  • Ch. Devchand and V. Ogievetsky -- Integrability of \(N=3\) super Yang-Mills equations
  • R. L. Dobrushin -- Estimates of semi-invariants for the Ising model at low temperatures
  • D. M. Gitman -- Pseudoclassical theory of a relativistic spinning particle
  • R. Kallosh -- Dual waves
  • V. P. Maslov and O. Yu. Shvedov -- Geometric quantization in the Fock space
  • R. Minlos and H. Spohn -- The three-body problem in radioactive decay: The case of one atom and at most two photons
  • M. I. Monastyrsky and S. M. Natanzon -- The moduli space of instantons in \(N=2\) supersymmetrical \(\sigma\)-models
  • A. Schwarz -- Superanalogs of symplectic and contact geometry and their applications to quantum field theory
  • Ya. G. Sinai and H. Spohn -- Remarks on the delocalization transition for heteropolymers
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