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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 |
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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 |
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Book DetailsContemporary MathematicsVolume: 219; 1998; 287 ppMSC: 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.
ReadershipMathematicians interested in mathematical and theoretical physics; advanced graduate students studying quantum field theory.
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Table of Contents
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Articles
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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 ]
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C. Becchi, S. Giusto and C. Imbimbo — The BRST structure of twisted $N=2$ algebra [ MR 1640442 ]
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L. Bonora, C. S. Chu and M. Rinaldi — Anomalies and locality in field theories and M-theory [ MR 1640443 ]
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Friedemann Brandt — Gauge covariant algebras and local BRST cohomology [ MR 1640444 ]
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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 ]
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Marc Henneaux — Consistent interactions between gauge fields: the cohomological approach [ MR 1640447 ]
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Niky Kamran and Thierry Robart — A compatible analytic manifold structure for Lie pseudogroups of infinite type [ MR 1640448 ]
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Joseph Krasil′shchik — Cohomology background in geometry of PDE [ MR 1640449 ]
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Nicola Maggiore — Algebraic renormalization of massive supersymmetric theories [ MR 1640450 ]
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G. Marmo and A. Ibort — A new look at completely integrable systems and double Lie groups [ MR 1640451 ]
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Vittorio Penna, Mario Rasetti and Mauro Spera — Quantum dynamics of 3-D vortices [ MR 1640452 ]
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Jim Stasheff — The (secret?) homological algebra of the Batalin-Vilkovisky approach [ MR 1640453 ]
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Alexander Verbovetsky — Notes on the horizontal cohomology [ MR 1640454 ]
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Claude M. Viallet — Invariants of rational transformations and algebraic entropy [ MR 1640455 ]
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Alexandre Vinogradov — Introduction to secondary calculus [ MR 1640456 ]
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Alexandre Vinogradov and Michael Vinogradov — On multiple generalizations of Lie algebras and Poisson manifolds [ MR 1640457 ]
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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Volume: 219; 1998; 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
Please select which format for which you are requesting permissions.