On the Relation Between Fock and Schroedinger Representations for a Scalar Field

Details On the Relation Between Fock and Schroedinger Representations for a Scalar Field On the Relation Between Fock and Schroedinger Representations for a Scalar Field

2002-02-11

arxiv.org/abs/hep-th/0202070v3

Annals Phys. 313 (2004) 446-478

Physics

High Energy Physics

High Energy Physics - Theory

23 pages. No figures. A new section on examples added

Scientific paper

10.1016/j.aop.2004.05.004

Linear free field theories are one of the few Quantum Field Theories that are exactly soluble. There are, however, (at least) two very different languages to describe them, Fock space methods and the Schroedinger functional description. In this paper, the precise sense in which the two representations are related is reviewed. Several properties of these representations are studied, among them the well known fact that the Schroedinger counterpart of the usual Fock representation is described by a Gaussian measure. A real scalar field theory is considered, both on Minkowski spacetime for arbitrary, non-inertial embeddings of the Cauchy surface, and for arbitrary (globally hyperbolic) curved spacetimes. As a concrete example, the Schroedinger representation on stationary and homogeneous cosmological spacetimes is constructed.

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