Deformation Theory and Symplectic Geometry
Springer (Verlag)
978-0-7923-4525-1 (ISBN)
The contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include authoritative, state-of-the-art contributions by leading scientists. New and important developments in the fields of symplectic geometry, deformation quantization, noncommutative geometry (NCG) and Lie theory are presented. Among the subjects treated are: quantization of general Poisson manifolds; new deformations needed for the quantization of Nambu mechanics; quantization of intersection cardinalities; quantum shuffles; new types of quantum groups and applications; quantum cohomology; strong homotopy Lie algebras; finite- and infinite-dimensional Lie groups; and 2D field theories and applications of NCG to gravity coupled with the standard model.
Audience: This book will be of interest to researchers and post-graduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, nonassociative rings and algebras, and Lie algebras.
Preface. Noncommutative Differential Geometry and the Structure of Space Time; A. Connes. Shift Operator for the Discrete sl(2) Current Algebra; L. Faddeev, A. Volkov. Nambu Mechanics, n-ary Operations and their Quantization; M. Flato, et al. The Geometrization Principle; J. Frohlich. Generalization and Deformations of Quantum Groups; C. Fronsdal. Quantized Intersection Cardinalities; M. Gerstenhaber. Deformation Quantization and Mpc Structures; S. Gutt, J. Rawnsley. Massless XXZ Model and Degeneration of the Elliptic Algebra Aq,p(sANDl2); M. Jimbo, et al. Formality Conjecture; M. Kontsevich. Quantum Cohomology of the Flag Manifold as an Algebra of Rational Functions on a Unipotent Algebraic Group; B. Kostant. Homologies Associated with Poisson Structures; O. Mathieu. Maximal Tori of Some Symplectomorphism Groups and Applications to Convexity; A. Bloch, et al. On 2D Yang-Mills Theory and Invariants of Links; M. Polyak, N. Reshetikhin. Some Applications of Quantum Shuffles; M. Rosso. Character Formulas and Localization of Integrals; W. Schmid. Deformation Theory and the Batalin-Vilkovisky Master Equation; J. Stasheff. The Fukaya Type Categories for Associative Algebras; R. Nest, B. Tsygan. Tangential Deformation Quantization and Polarized Symplectic Groupoids; A. Weinstein. Formal GNS Construction and WKB Expansion in Deformation Quantization; M. Bordemann, S. Waldmann. On the Deformation of Time Harmonic Flows; J. Hoppe. Distinguished Essential Extensions of Infinite Dimensional Classical Lie Algebras; A. Lichnerowicz. Noncommutative Contact Algebras; H. Omori, et al. Braided Geometry and the Inductive Construction of Lie Algebras and Quantum Groups; S. Majid. Star Products in the Triangular Case; C. Moreno, L. Valero. Aspetti fisici della teoria delle deformazioni; G. Dito. Scientific Programme. List of Participants.
| Reihe/Serie | Mathematical Physics Studies ; 20 |
|---|---|
| Zusatzinfo | XIII, 368 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| ISBN-10 | 0-7923-4525-8 / 0792345258 |
| ISBN-13 | 978-0-7923-4525-1 / 9780792345251 |
| Zustand | Neuware |
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