Contemporary Mathematics 1998; 287 pp; softcover Volume: 219 ISBN10: 0821808281 ISBN13: 9780821808283 List Price: US$72 Member Price: US$57.60 Order Code: CONM/219
 This collection of invited lectures (at the Conference on Secondary Calculus and Cohomological Physics, Moscow) reflects the stateoftheart in a new branch of mathematics and mathematical physics arising at the intersection of geometry of nonlinear differential equations, quantum field theory, and cohomological algebra. This is the first comprehensive and selfcontained book on modern quantum field theory in the context of cohomological methods and the geometry of nonlinear PDEs. Features:  An uptodate and selfcontained exposition of the newest results in cohomological aspects of quantum field theory and the geometry of PDEs.
 A new look at interrelations among cohomology theory, the geometry of PDEs, and field theory.
 Application to BatalinVilkovisky formalism, BRST formalism, anomalies, and quantum dynamics.
Readership Mathematicians interested in mathematical and theoretical physics; advanced graduate students studying quantum field theory. Table of Contents  M. Asorey, F. Falceto, and G. Luzón  Unstable bundles in quantum field theory
 G. Barnich  Brackets in the jetbundle approach to field theory
 C. Becchi, S. Giusto, and C. Imbimbo  The BRST structure of twisted \(N = 2\) algebra
 L. Bonora, C. S. Chu, and M. Rinaldi  Anomalies and locality in field theories and Mtheory
 F. Brandt  Gauge covariant algebras and local BRST cohomology
 M. DuboisViolette  Generalized homologies for \(d^N = 0\) and graded \(q\)differential algebras
 M. Fliess, J. Lévine, P. Martin, and P. Rouchon  Nonlinear control and diffieties, with an application to physics
 M. Henneaux  Consistent interactions between gauge fields: the cohomological approach
 N. Kamran and T. Robart  A compatible analytic manifold structure for Lie pseudogroups of infinite type
 J. Krasil'shchik  Cohomology background in geometry of PDE
 N. Maggiore  Algebraic renormalization of massive supersymmetric theories
 G. Marmo and A. Ibort  A new look at completely integrable systems and double Lie groups
 V. Penna, M. Rasetti, and M. Spera  Quantum dynamics of 3D vortices
 J. D. Stasheff  The (secret?) homological algebra of the BatalinVilkovisky approach
 A. Verbovetsky  Notes on the horizontal cohomology
 C. M. Viallet  Invariants of rational transformations and algebraic entropy
 A. Vinogradov  Introdution to secondary calculus
 A. Vinogradov and M. Vinogradov  On multiple generalizations of Lie algebras and Poisson manifolds
