This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

Quantum Fields in Curved Space

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Sur certains groupes d'opérateurs unitaires

We construct projective unitary representations of (a) Map(S1;G), the group of smooth maps from the circle into a compact Lie groupG, and (b) the group of diffeomorphisms of the circle. We show that a class of representations of Map(S1;T), whereT is a maximal torus ofG, can be extended to representations of Map(S1;G),

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Unitary representations of some infinite-dimensional groups

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.

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Remarks on classical invariant theory

Symmetries of some reduced free product C*-algebras

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David Shale

Papers

Linear symmetries of free boson fields(

States of the Clifford Algebra

Wiener processes II

Invariant integration over the infinite dimensional orthogonal group and related spaces

The quantum harmonic oscillator with hyperbolic phase space