| | Contemporary Mathematics
1998; 287 pp; softcover
ISBN-13: 978-0-8218-0828-3 List Price: US$76
Member Price: US$60.80
Order Code: CONM/219
This collection of invited lectures (at the Conference on Secondary Calculus and Cohomological Physics, Moscow) reflects the state-of-the-art 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 self-contained book on modern quantum field theory in the context of cohomological methods and the geometry of nonlinear PDEs.
- An up-to-date and self-contained 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 Batalin-Vilkovisky formalism, BRST formalism, anomalies, and quantum dynamics.
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 jet-bundle 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 M-theory
- F. Brandt -- Gauge covariant algebras and local BRST cohomology
- M. Dubois-Violette -- 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 3-D vortices
- J. D. Stasheff -- The (secret?) homological algebra of the Batalin-Vilkovisky 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