Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time

Stephen A. Fulling
Phys. Rev. D 7, 2850 – Published 15 May 1973
PDFExport Citation

Abstract

We point out and discuss an ambiguity which arises in the quantum theory of fields when the background metric is not explicitly Minkowskian-in other words, when an external gravitational field, real or apparent, is present. A general theory of a canonical neutral scalar field in a static universe, including the construction of a Fock space, is presented. It is applied to a portion of two-dimensional flat space-time equipped with a non-Cartesian space-time coordinate system with respect to which the metric is nonetheless static. The resulting particle interpretation of the field is shown to be different from the standard one in special-relativistic free-field theory. The ambiguity frustrates an attempt to define uniquely the energy-momentum tensor by the usual method of normal ordering. We discuss various suggestions for (1) distinguishing a unique correct quantization in a given physical situation, or (2) reinterpreting seemingly inequivalent theories as physically equivalent. In passing it is shown that the vacuum state and the energy density of a free field in a box with periodic boundary conditions differ from those associated with a region of the same size in infinite space; this result should be of interest outside the gravitational context.

  • Received 3 November 1972

DOI:https://doi.org/10.1103/PhysRevD.7.2850

©1973 American Physical Society

Authors & Affiliations

Stephen A. Fulling*

  • University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

  • *NSF Graduate Fellow, Princeton University, 1967-71.

References (Subscription Required)

Click to Expand
Issue

Vol. 7, Iss. 10 — 15 May 1973

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×