Geometry and physics / by Jurgen Jost.

Format:

Book

Author/Creator:

Jost, Jürgen, 1956-

Contributor:

Class of 1932 Fund.

Language:

English

Subjects (All):

Geometry, Differential.

Mathematical physics.

Quantum theory.

Physical Description:

xiv, 217 pages : illustrations ; 24 cm

Place of Publication:

Heidelberg ; London : Springer, [2009]

Summary:

Geometry and Physics addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics.

Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.

Contents:

1 Geometry 1

1.1 Riemannian and Lorentzian Manifolds 1

1.1.1 Differential Geometry 1

1.1.2 Complex Manifolds 13

1.1.3 Riemannian and Lorentzian Metrics 17

1.1.4 Geodesies 21

1.1.5 Curvature 26

1.1.6 Principles of General Relativity 29

1.2 Bundles and Connections 33

1.2.1 Vector and Principal Bundles 33

1.2.2 Covariant Derivatives 37

1.2.3 Reduction of the Structure Group. The Yang-Mills Functional 41

1.2.4 The Kaluza-Klein Construction 47

1.3 Tensors and Spinors 49

1.3.1 Tensors 49

1.3.2 Clifford Algebras and Spinors 50

1.3.3 The Dirac Operator 56

1.3.4 The Lorentz Case 57

1.3.5 Left- and Right-handed Spinors 61

1.4 Riemann Surfaces and Moduli Spaces 63

1.4.1 The General Idea of Moduli Spaces 63

1.4.2 Riemann Surfaces and Their Moduli Spaces 64

1.4.3 Compactifications of Moduli Spaces 78

1.5 Supermanifolds 83

1.5.1 The Functorial Approach 83

1.5.2 Supermanifolds 85

1.5.3 Super Riemann Surfaces 90

1.5.4 Super Minkowski Space 94

2 Physics 97

2.1 Classical and Quantum Physics 97

2.1.1 Introduction 97

2.1.2 Gaussian Integrals and Formal Computations 101

2.1.3 Operators and Functional Integrals 107

2.1.4 Quasiclassical Limits 117

2.2 Lagrangians 121

2.2.1 Lagrangian Densities for Scalars, Spinors and Vectors 121

2.2.2 Scaling 128

2.2.3 Elementary Particle Physics and the Standard Model 131

2.2.4 The Higgs Mechanism 135

2.2.5 Supersymmetric Point Particles 139

2.3 Variational Aspects 146

2.3.1 The Euler-Lagrange Equations 146

2.3.2 Symmetries and Invariances: Noether's Theorem 147

2.4 The Sigma Model 151

2.4.1 The Linear Sigma Model 151

2.4.2 The Nonlinear Sigma Model 156

2.4.3 The Supersymmetric Sigma Model 158

2.4.4 Boundary Conditions 163

2.4.5 Supersymmetry Breaking 166

2.4.6 The Supersymmetric Nonlinear Sigma Model and Morse Theory 170

2.4.7 The Gravitino 178

2.5 Functional Integrals 181

2.5.1 Normal Ordering and Operator Product Expansions 182

2.5.2 Noether's Theorem and Ward Identities 187

2.5.3 Two-dimensional Field Theory 189

2.6 Conformal Field Theory 194

2.6.1 Axioms and the Energy-Momentum Tensor 194

2.6.2 Operator Product Expansions and the Virasoro Algebra 198

2.6.3 Superfields 199

2.7 String Theory 204.

Notes:

Includes bibliographical references (pages 209-212) and index.

Includes index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1932 Fund.

ISBN:

9783642005404

3642005403

3642005411

9783642005411

OCLC:

457179274