Analysis of interacting quantum field theory in curved spacetime

Journal Article · Tue Jul 01 04:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524622· OSTI ID:5336291

Birrell, N D; Taylor, J G

A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green's functions are derived, special attention being paid to the possibility that the ''in'' and ''out'' vacuum states may not be equivalent. Green's functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for lambdaphi/sup 3//sub() 4,6/ field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, phi/sup 3//sub(/sub 4/) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes.

• Research Organization: Department of Mathematics, University of London, King's College, Strand, London WC2R 2LS, United Kingdom
• OSTI ID: 5336291
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY-VALUE PROBLEMS
FIELD THEORIES
FUNCTIONS
GRAVITATIONAL FIELDS
GREEN FUNCTION
MATHEMATICAL SPACE
MATRICES
MINKOWSKI SPACE
PARTICLE PRODUCTION
QUANTUM FIELD THEORY
RENORMALIZATION
S MATRIX
SPACE
SPACE-TIME
VACUUM STATES