Regularization and renormalization of quantum field theory in curved space-time

Journal Article · Tue Sep 06 04:00:00 EDT 1977 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(77)90210-X· OSTI ID:7076914

Bernard, C; Duncan, A

It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli--Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by always starting from a manifestly generally covariant action, and the technical limitations of the dimensional regularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions, it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli--Villars regulated. We then study a specific solvable two-dimensional model of a massive scalar field in a Robertson--Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well-defined finite expectation value for the stress-energy tensor. The particle production (<0 in vertical-bartheta/sup munu( x ,t)/vertical-bar0 in> for t..-->..+infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t..-->.. +- infinity independently of any weak-field approximation. The extension of our model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed.

• Research Organization: Department of Physics, Columibia University, New York, New York 10027
• OSTI ID: 7076914
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 107:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
FIELD THEORIES
INTERACTIONS
MATHEMATICAL MODELS
NUCLEAR MODELS
PARTICLE INTERACTIONS
PARTICLE PRODUCTION
PERTURBATION THEORY
QUANTUM FIELD THEORY
RENORMALIZATION
SPACE-TIME
TWO-DIMENSIONAL CALCULATIONS
WEAK-COUPLING MODEL