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Secondary Calculus and Cohomological Physics
Edited by: Marc Henneaux, Université Libre de Bruxelles, Brussels, Belgium, Joseph Krasil'shchik, Moscow Institute for Municipal Economy, Russia, and Alexandre Vinogradov, University of Salerno, Italy

Contemporary Mathematics
1998; 287 pp; softcover
Volume: 219
ISBN-10: 0-8218-0828-1
ISBN-13: 978-0-8218-0828-3
List Price: US$72
Member Price: US$57.60
Order Code: CONM/219
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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.


  • 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
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