Secondary Calculus and Cohomological Physics

Secondary Calculus and Cohomological Physics

by Marc Henneaux, A. M. Vinogradov, I. S. Krasil-Shchik
     
 

ISBN-10: 0821808281

ISBN-13: 9780821808283

Pub. Date: 07/16/1998

Publisher: American Mathematical Society

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

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Overview

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. Features: 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.

Product Details

ISBN-13:
9780821808283
Publisher:
American Mathematical Society
Publication date:
07/16/1998
Series:
Contemporary Mathematics Series, #219
Pages:
287
Product dimensions:
7.05(w) x 10.12(h) x (d)

Table of Contents

Acknowledgments
Foreword
Unstable bundles in quantum field theory1
Brackets in the jet-bundle approach to field theory17
The BRST structure of twisted N = 2 algebra29
Anomalies and locality in field theories and M-theory39
Gauge covariant algebras and local BRST cohomology53
Generalized homologies for d[superscript N] = 0 and graded q-differential algebras69
Nonlinear control and diffieties, with an application to physics81
Consistent interactions between gauge fields: the cohomological approach93
A compatible analytic manifold structure for Lie pseudogroups of infinite type111
Cohomology background in geometry of PDE121
Algebraic renormalization of massive supersymmetric theories141
A new look at completely integrable systems and double Lie groups159
Quantum dynamics of 3-D vortices173
The (secret?) homological algebra of the Batalin - Vilkovisky approach195
Notes on the horizontal cohomology211
Invariants of rational transformations and algebraic entropy233
Introduction to Secondary Calculus241
On multiple generalizations of Lie algebras and Poisson manifolds273

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