Analysis, manifolds and physics. Part II / by Yvonne Choquet-Bruhat, Cécile DeWitt-Morette.

Format:

Book

Author/Creator:

Choquet-Bruhat, Yvonne.

Contributor:

DeWitt-Morette, Cécile.

ScienceDirect (Online service)

Language:

English

Subjects (All):

Mathematical analysis.

Manifolds (Mathematics).

Mathematical physics.

Physical Description:

1 online resource (xvi, 541 pages) : illustrations.

Edition:

Rev. and enl. ed.

Place of Publication:

Amsterdam ; New York : Elsevier, 2000.

Contents:

Cover

Preface to the second edition

Preface

Contents

Conventions

CHAPTER I. REVIEW OF FUNDAMENTAL NOTIONS OF ANALYSIS

1. Graded algebras

2. Berezinian

3. Tensor product of algebras

4. Clifford algebras

5. Clifford algebra as a coset of the tensor algebra

6. Fierz identity

7. Pin and Spin groups

8. Weyl spinors, helicity operator; Majorana pinors, charge conjugation

9. Representations of Spin(n, m), n + m odd

10. Dirac adjoint

11. Lie algebra of Pin(n, m) and Spin(n, m)

12. Compact spaces

13. Compactness in weak star topology

14. Homotopy groups, general properties

15. Homotopy of topological groups

16. Spectrum of closed and self-adjoint linear operators

CHAPTER II. DIFFERENTIAL CALCULUS ON BANACH SPACES

1. Supersmooth mappings

2. Berezin integration; Gaussian integrals

3. Noether's theorems I

4. Noether's theorems II

5. Invariance of the equations of motion

6. String action

7. Stress-energy tensor; energy with respect to a timelike vector field

CHAPTER III. DIFFERENTIABLE MANIFOLDS

1. Sheaves

2. Differentiable submanifolds

3. Subgroups of Lie groups. When are they Lie subgroups?

4. Cartan-Killing form on the Lie algebra g of a Lie group G

5. Direct and semidirect products of Lie groups and their Lie algebra

6. Homomorphisma and anthihomomorphisms of a life algebra into spaces of vector fields

7. Homogeneous spaces; symmetric spaces

8. Examples of homogeneous spaces, Stiefel and Grassmann manifolds

9. Abelian representations of nonabelian groups

10. Irreducibility and reducibility

11. Characters

12. Solvable Lie groups

13. Lie algebras of linear groups

14. Graded bundles

CHAPTER IV. INTEGRATION ON MANIFOLDS

1. Cohomology. Definitions and exercises

2. Obstruction to the construction of Spin and Pin bundles; Stiefel-Whitney classes

3. Inequivalent spin structures

4. Cohomology of groups

5. Lifting a group action

6. Short exact sequence; Weyl Heisenberg group

7. Cohomology of Lie algebras

8. Quasi-linear first-order partial differential equation

9. Exterior differential systems

10. Bäcklund transformations for evolution equations

11. Poisson manifolds I

12. Poisson manifolds II

13. Completely integrable systems

CHAPTER V. RIEMANNIAN MANIFOLDS. KÄHLERIAN MANIFOLDS

1. Necessary and sufficient conditions for Lorentzian signature

2. First fundamental form (induced metric)

3. Killing vector fields

4. Sphere Sn

5. Curvature of Einstein cylinder

6. Conformal transformation of Yang-Mills, Dirac and Higgs operators in d dimensions

7. Conformal system for Einstein equations

8. Conformal transformation of nonlinear wave equations

9. Masses of "homothetic" space-time

10. Invariant geometries on the squashed seven spheres

11. Harmonic maps

12. Composition of maps

13. Kaluz.

Notes:

Companion volume to: Analysis, manifolds and physics. Rev. ed. 1982.

Includes bibliographical references and index.

Electronic reproduction. Amsterdam Available via World Wide Web.

Description based on print version record.

Other Format:

Online version: Choquet-Bruhat, Yvonne. Analysis, manifolds and physics. Part II.

ISBN:

9780080527154 (electronic bk.)

0080527159 (electronic bk.)

Publisher Number:

99994695474

Access Restriction:

Restricted for use by site license.