Analysis, manifolds and physics

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Bibliographic Information

Analysis, manifolds and physics

by Yvonne Choquet-Bruhat, Cécile DeWitt-Morette, with Margaret Dillard-Bleick

North-Holland, 1982-1989

Rev. ed

  • pt. 1, Basics
  • pt. 2, 92 applications

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Note

Includes bibliographical references and index

"... companion volume to our first book, Analysis, manifolds and physics, (revised edition 1982)"--Pt. 2, pref.

Description and Table of Contents

Volume

pt. 1, Basics ISBN 9780444860170

Description

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

Table of Contents

Preface. Chapters: I. Review of fundamental notions of analysis. II. Differential calculus on Banach spaces. III. Differentiable manifolds, finite dimensional case. IV. Integration on manifolds. V. Riemannian manifolds. Kahlerian manifolds. V bis. Connections on a principle fibre bundle. VI. Distributions. VII. Differentiable manifolds, infinite dimensional case. References. Symbols. Index.
Volume

pt. 2, 92 applications ISBN 9780444870711

Description

This second, companion volume contains 92 applications developing concepts and theorems presented or mentioned in the first volume. Introductions to and applications in several areas not previously covered are also included such as graded algebras with applications to Clifford algebras and (S)pin groups, Weyl Spinors, Majorana pinors, homotopy, supersmooth mappings and Berezin integration, Noether's theorems, homogeneous spaces with applications to Stiefel and Grassmann manifolds, cohomology with applications to (S)pin structures, Backlund transformations, Poisson manifolds, conformal transformations, Kaluza-Klein theories, Calabi-Yau spaces, universal bundles, bundle reduction and symmetry breaking, Euler-Poincare characteristics, Chern-Simons classes, anomalies, Sobolev embedding, Sobolev inequalities, Wightman distributions and Schwinger functions. The material included covers an unusually broad area and the choice of problems is guided by recent applications of differential geometry to fundamental problems of physics as well as by the authors' personal interests.

Table of Contents

Preface. I. Review of fundamental notions of analysis. II. Differential calculus on Banach spaces. III. Differentiable manifolds. IV. Integration on manifolds. V. Riemannian manifolds. Kahlerian manifolds. V bis. Connections on a principal fibre bundle. VI. Distributions. Subject Index.

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