Secondary Calculus and Cohomological Physics

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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.

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Editorial Reviews

Booknews
The 18 invited lectures explore a new branch of mathematics and mathematical physics arising from the intersection of the geometry of nonlinear differential equations, quantum field theory, and cohomological algebra. They include recent results in cohomological aspects of quantum field theory and the geometry of partial differential equations; a new look at interrelations among the related fields; and applications to Batalin-Vilkovisky formalism, BRST formalism, anomalies, and quantum dynamics. Accessible to professional and advanced graduate mathematicians. No index. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

Acknowledgments
Foreword
Unstable bundles in quantum field theory 1
Brackets in the jet-bundle approach to field theory 17
The BRST structure of twisted N = 2 algebra 29
Anomalies and locality in field theories and M-theory 39
Gauge covariant algebras and local BRST cohomology 53
Generalized homologies for d[superscript N] = 0 and graded q-differential algebras 69
Nonlinear control and diffieties, with an application to physics 81
Consistent interactions between gauge fields: the cohomological approach 93
A compatible analytic manifold structure for Lie pseudogroups of infinite type 111
Cohomology background in geometry of PDE 121
Algebraic renormalization of massive supersymmetric theories 141
A new look at completely integrable systems and double Lie groups 159
Quantum dynamics of 3-D vortices 173
The (secret?) homological algebra of the Batalin - Vilkovisky approach 195
Notes on the horizontal cohomology 211
Invariants of rational transformations and algebraic entropy 233
Introduction to Secondary Calculus 241
On multiple generalizations of Lie algebras and Poisson manifolds 273
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