Aspects of quantum field theory in curved space-time / Stephen A. Fulling.

Includes bibliographical references (pages 287-301) and index.

Print version record.

The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.

Cover; Series Page; Title; Copyright; Contents; Preface; Chapter 1 A Quick Course in Quantum Mechanics; CLASSICAL MECHANICS: THE CANONICAL FORMALISM; QUANTUM STATES AND OBSERVABLES; QUANTUM DYNAMICS: THE HEISENBERG PICTURE; THE SCHRODINGER PICTURE; THE CONNECTION BETWEEN THE TWO PICTURES; THE CLASSICAL LIMIT; RESPECTIVE ADVANTAGES OF THE TWO PICTURES; Chapter 2 Self-Adjoint, Elliptic Differential Operators and Eigenfunction Expansions; DEFINITIONS; SELF-ADJOINT EXTENSIONS: THE CLASSIC EXAMPLES; THE SPECTRAL THEOREM; THE PROBLEM OF EIGENFUNCTION EXPANSION; THE WEYL-TITCHMARSH-KODAIRA THEORY

SOLUTION TO EXERCISE 2Chapter 3 Quantization of a Static, Scalar Field Theory; POSITIVE-FREQUENCY SOLUTIONS; THE NEWTON-WIGNER POSITION OPERATOR; FOCK SPACE; FIELD OPERATORS; Chapter 4 Two-Point Functions; GREEN FUNCTIONS; TWO-POINT FUNCTIONS OF A QUANTUM FIELD; A DISTRIBUTIONAL TREATMENT; MATHEMATICAL INTERPRETATION OF SINGULARITIES; RECONSTRUCTION OF THE FIELD THEORY; Chapter 5 The Stress Tensor and the Casimir Effect; FIELD OBSERVABLES; THE CASIMIR EFFECT; CALCULATIONS OF ENERGY DENSITY; SOME HISTORY AND SOME CONTACT WITH THE REAL WORLD; LESSONS FROM THE CASIMIR EFFECT

Chapter 6 Quantum Field Theory in General Space-TimesCANONICAL FORMALISM; GLOBAL HYPERBOLICITY; GENERAL CONSIDERATIONS; SPECIALIZATION OF THE GENERAL FORMALISM TO THE STATIC CASE; Chapter 7 Quantum Field Theory in an Expanding U ni verse; PRELIMIN ARIES; GENERAL BOGOLUBOV TRANSFORMATIONS; STIMULATED EMISSION; SPIN AND STATISTICS; PARTICLE OBSERVABLES AT FINITE TIMES; THE ADIABATIC APPROACH; Chapter 8 Some Geometrical Apparatus; COVARIANT DERIVATIVES; CURVATURE; PARALLEL TRANSPORT AND GEODESIC DISTANCE; COVARIANT POWER SERIES; RECURSIVE CALCULATIONS OF THE SYNGE-DEWITT TENSORS

Chapter 9 Renormalization of the Stress TensorWALD'S AXIOMATIC ANALYSIS; HAMIDEW THEORY; THE HEAT KERNEL; FURTHER REMARKS ON THE HEAT KERNEL; HYPERBOLIC AND ELLIPTIC GREEN FUNCTIONS; VINDICATION: THE UNIVERSALITY THEOREM; RENORMALIZATION PRESCRIPTIONS; UNIQUENESS ISSUES; Conclusion; Appendix: Varieties of Instability of a Boson Field in an External Potential and Black Hole Klein Paradoxes; Abstract; Part One; Part Two; Acknowledgments; Bibliography; Index

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