Quantum field theory on curved spacetimes : concepts and mathematical foundations / C . Bär, K. Fredenhagen (eds.).

Format:

Book

Contributor:

Bär, Christian.

Fredenhagen, K. (Klaus)

Series:

Lecture notes in physics ; 786.

Lecture notes in physics, 0075-8450 ; 786

Language:

English

Subjects (All):

Quantum field theory.

Space and time.

Physical Description:

x, 160 pages : illustrations ; 24 cm.

Place of Publication:

Berlin : New York : Springer, 2009.

Summary:

After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. These, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes.

Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as wells as more recently the insights from suitable concepts such as microlocal analysis.

This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader.

Contents:

1 C*-algebras / Christian Br̃, Christian Becker 1

1.1 Basic Definitions 1

1.2 The Spectrum 4

1.3 Morphisms 12

1.4 States and Representations 16

1.5 Product States 23

1.6 Weyl Systems 29

References 36

2 Lorentzian Manifolds / Frank Pfäffie 39

2.1 Preliminaries on Minkowski Space 39

2.2 Lorentzian Manifolds 40

2.3 Time-Orientation and Causality Relations 43

2.4 Causality Condition and Global Hyperbolicity 52

2.5 Cauchy Hypersurfaces 55

References 58

3 Linear Wave Equations / Nicolas Ginoux 59

3.1 Introduction 59

3.2 General Setting 60

3.3 Riesz Distributions on the Minkowski Space 64

3.4 Local Fundamental Solutions 68

3.5 The Cauchy Problem and Global Fundamental Solutions 72

3.6 Green's Operators 81

References 84

4 Microlocal Analysis / Alexander Strohmaier 85

4.1 Introduction 85

4.2 Distributions 86

4.3 Singularities of Distributions and the Wavefront Set 98

4.4 Differential Operators, the Wave Equation, and Further Properties of the Wavefront Set 119

4.5 Wavefront Set of Propagators in Curved Spacetimes 122

References 127

5 Quantum Field Theory on Curved Backgrounds / Romeo Brunetti, Klaus Fredenhagen 129

5.1 Introduction 129

5.2 Systems and Subsystems 130

5.3 Locally Covariant Theories 134

5.4 Classical Field Theory 137

5.5 Quantum Field Theory 144

References 154.

Notes:

Includes bibliographical references and index.

ISBN:

9783642027796

3642027792

OCLC:

428028984