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Secondary Calculus and Cohomological Physics
 
Edited by: Marc Henneaux Université Libre de Bruxelles, Brussel, Belgium
Joseph Krasil′shchik Moscow Institute for Municipal Economy, Moscow, Russia
Alexandre Vinogradov University of Salerno, Salerno, Italy
Secondary Calculus and Cohomological Physics
eBook ISBN:  978-0-8218-7810-1
Product Code:  CONM/219.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Secondary Calculus and Cohomological Physics
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Secondary Calculus and Cohomological Physics
Edited by: Marc Henneaux Université Libre de Bruxelles, Brussel, Belgium
Joseph Krasil′shchik Moscow Institute for Municipal Economy, Moscow, Russia
Alexandre Vinogradov University of Salerno, Salerno, Italy
eBook ISBN:  978-0-8218-7810-1
Product Code:  CONM/219.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 2191998; 287 pp
    MSC: Primary 81; 35; Secondary 58;

    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.
    Readership

    Mathematicians interested in mathematical and theoretical physics; advanced graduate students studying quantum field theory.

  • Table of Contents
     
     
    • Articles
    • M. Asorey, F. Falceto and G. Luzón — Unstable bundles in quantum field theory [ MR 1640440 ]
    • Glenn Barnich — Brackets in the jet-bundle approach to field theory [ MR 1640441 ]
    • C. Becchi, S. Giusto and C. Imbimbo — The BRST structure of twisted $N=2$ algebra [ MR 1640442 ]
    • L. Bonora, C. S. Chu and M. Rinaldi — Anomalies and locality in field theories and M-theory [ MR 1640443 ]
    • Friedemann Brandt — Gauge covariant algebras and local BRST cohomology [ MR 1640444 ]
    • Michel Dubois-Violette — Generalized homologies for $d^N=0$ and graded $q$-differential algebras [ MR 1640445 ]
    • Michel Fliess, Jean Lévine, Philippe Martin and Pierre Rouchon — Nonlinear control and diffieties, with an application to physics [ MR 1640446 ]
    • Marc Henneaux — Consistent interactions between gauge fields: the cohomological approach [ MR 1640447 ]
    • Niky Kamran and Thierry Robart — A compatible analytic manifold structure for Lie pseudogroups of infinite type [ MR 1640448 ]
    • Joseph Krasil′shchik — Cohomology background in geometry of PDE [ MR 1640449 ]
    • Nicola Maggiore — Algebraic renormalization of massive supersymmetric theories [ MR 1640450 ]
    • G. Marmo and A. Ibort — A new look at completely integrable systems and double Lie groups [ MR 1640451 ]
    • Vittorio Penna, Mario Rasetti and Mauro Spera — Quantum dynamics of 3-D vortices [ MR 1640452 ]
    • Jim Stasheff — The (secret?) homological algebra of the Batalin-Vilkovisky approach [ MR 1640453 ]
    • Alexander Verbovetsky — Notes on the horizontal cohomology [ MR 1640454 ]
    • Claude M. Viallet — Invariants of rational transformations and algebraic entropy [ MR 1640455 ]
    • Alexandre Vinogradov — Introduction to secondary calculus [ MR 1640456 ]
    • Alexandre Vinogradov and Michael Vinogradov — On multiple generalizations of Lie algebras and Poisson manifolds [ MR 1640457 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2191998; 287 pp
MSC: Primary 81; 35; Secondary 58;

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.
Readership

Mathematicians interested in mathematical and theoretical physics; advanced graduate students studying quantum field theory.

  • Articles
  • M. Asorey, F. Falceto and G. Luzón — Unstable bundles in quantum field theory [ MR 1640440 ]
  • Glenn Barnich — Brackets in the jet-bundle approach to field theory [ MR 1640441 ]
  • C. Becchi, S. Giusto and C. Imbimbo — The BRST structure of twisted $N=2$ algebra [ MR 1640442 ]
  • L. Bonora, C. S. Chu and M. Rinaldi — Anomalies and locality in field theories and M-theory [ MR 1640443 ]
  • Friedemann Brandt — Gauge covariant algebras and local BRST cohomology [ MR 1640444 ]
  • Michel Dubois-Violette — Generalized homologies for $d^N=0$ and graded $q$-differential algebras [ MR 1640445 ]
  • Michel Fliess, Jean Lévine, Philippe Martin and Pierre Rouchon — Nonlinear control and diffieties, with an application to physics [ MR 1640446 ]
  • Marc Henneaux — Consistent interactions between gauge fields: the cohomological approach [ MR 1640447 ]
  • Niky Kamran and Thierry Robart — A compatible analytic manifold structure for Lie pseudogroups of infinite type [ MR 1640448 ]
  • Joseph Krasil′shchik — Cohomology background in geometry of PDE [ MR 1640449 ]
  • Nicola Maggiore — Algebraic renormalization of massive supersymmetric theories [ MR 1640450 ]
  • G. Marmo and A. Ibort — A new look at completely integrable systems and double Lie groups [ MR 1640451 ]
  • Vittorio Penna, Mario Rasetti and Mauro Spera — Quantum dynamics of 3-D vortices [ MR 1640452 ]
  • Jim Stasheff — The (secret?) homological algebra of the Batalin-Vilkovisky approach [ MR 1640453 ]
  • Alexander Verbovetsky — Notes on the horizontal cohomology [ MR 1640454 ]
  • Claude M. Viallet — Invariants of rational transformations and algebraic entropy [ MR 1640455 ]
  • Alexandre Vinogradov — Introduction to secondary calculus [ MR 1640456 ]
  • Alexandre Vinogradov and Michael Vinogradov — On multiple generalizations of Lie algebras and Poisson manifolds [ MR 1640457 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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