Aspects of Quantum Field Theory in Curved Spacetime
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.
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algebra angular momentum annihilation antiparticle asymptotic basis behavior black hole Bogolubov transformation boundary conditions calculation canonical canonical commutation relations Casimir Cauchy surface Chapter charge classical coefficients commutation relations complex coordinate covariant derivative curved space-time defined definition density differential equation differential operator dimension eigenfunctions eigenvalue eigenvectors electromagnetic elliptic energy equation of motion equivalent expansion expectation value field equation finite Fock space formalism formula frequencies gauge geodesic geometry globally hyperbolic gravitational field Green functions Hamiltonian hence Hermitian Hilbert space integral Klein paradox light cone linear manifold metric negative norm notation observables pair particle creation Phys physical potential problem quantization quantum field theory quantum theory region renormalization representation satisfy scalar field Schrodinger self-adjoint self-adjoint operator smooth solution spectral spectral theorem square-integrable static stress tensor symmetric theorem time-dependent tion vacuum variables vector wave equation wave function