Schrödinger representation for a scalar field on curved spacetime

Alejandro Corichi, Jerónimo Cortez, and Hernando Quevedo
Phys. Rev. D 66, 085025 – Published 30 October 2002
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Abstract

It is generally known that linear (free) field theories are one of the few quantum field theories that are exactly soluble. In the Schrödinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the usual Fock representation is described by a Gaussian measure. In this paper, arbitrary globally hyperbolic spacetimes and embeddings of the Cauchy surface are considered. The classical structures relevant for quantization are used for constructing the Schrödinger representation in the general case. It is shown that, in this case, the measure is also Gaussian. Possible implications for the program of canonical quantization of midisuperspace models are pointed out.

  • Received 25 July 2002

DOI:https://doi.org/10.1103/PhysRevD.66.085025

©2002 American Physical Society

Authors & Affiliations

Alejandro Corichi*

  • Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México D.F. 04510, México,
  • Department of Physics and Astronomy, University of Mississippi, University, Mississippi 38677,
  • Perimeter Institute for Theoretical Physics, 35 King Road North, Waterloo, Ontario, Canada N2J 2W9

Jerónimo Cortez and Hernando Quevedo

  • Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México D.F. 04510, México

  • *Email address: corichi@nuclecu.unam.mx
  • Email address: cortez@nuclecu.unam.mx
  • Email address: quevedo@nuclecu.unam.mx

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Issue

Vol. 66, Iss. 8 — 15 October 2002

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