Description
Book SynopsisThe 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 knowle
Trade Review"...an excellent introduction to the research of the past two decades bearing on this test problem." American Scientist
"It provides for the mathematician an introduction to this field of physics in a language and from a point of view which we quickly find familiar. The physicist will gain the conviction that this quantum field theory has a very sound mathematical basis." Sorin Marculescu, Mathematical Reviews
Table of ContentsPreface; 1. A quick course in quantum mechanics; 2. Self-adjoint, elliptic differential operators and eigen-function expansions; 3. Quantisation of a static, scalar field theory; 4. Two-point functions; 5. The stress tensor and the Casimir effect; 6. Quantum field theory in general space-times; 7. Quantum field theory in an expanding universe; 8. Some geometrical apparatus; 9. Renormalisation of the stress tensor; Conclusion; Appendix; Bibliography; Index.
