Effective Lagrangian for lambdaphi/sup 4/ theory in curved spacetime with varying background fields: Quasilocal approximation

Journal Article · Wed Aug 15 04:00:00 EDT 1984 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.30.743· OSTI ID:6444595

Hu, B L; O'Connor, D J

By means of a Riemann normal coordinate expansion for the metric and a momentum-space representation for the Green's function, we derive in analytic form the one-loop effective Lagrangian for a lambdaphi/sup 4/ theory in curved spacetime which is exact to all orders in lambda and includes variation of the background field up to the second order. Ultraviolet divergences are removed by small-proper-time expansion and dimensional regularization. We obtain a generalized expression for the a/sub 2/ Minakshisundaram-DeWitt coefficient of the scalar wave operator with spacetime-dependent background field. A set of renormalization-group equations for the coupling constants of the theory is obtained, which can be used for analyzing their curvature and energy dependence. An alternative derivation of the effective Lagrangian is presented via the heat-kernel technique for anisotropic harmonic oscillators. Our result is useful for the study of quantum processes in the early universe or black holes under conditions where spacetime curvature and dynamical field effects are important. When suitably generalized, the effective Lagrangian obtained here in the form of a quasipotential should provide an improvement over the flat-space Coleman-Weinberg potential assumed in most discussions of the new inflationary universe. Possible directions for developing our method for more general problems are also discussed.

• Research Organization: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
• OSTI ID: 6444595
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 30:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640106 -- Astrophysics & Cosmology-- Cosmology
645400* -- High Energy Physics-- Field Theory
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
COSMOLOGICAL MODELS
COUPLING CONSTANTS
FIELD THEORIES
FUNCTIONS
GRAND UNIFIED THEORY
GREEN FUNCTION
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
PARTICLE MODELS
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
QUANTUM GRAVITY
RENORMALIZATION
SPACE-TIME
UNIFIED GAUGE MODELS
UNIFIED-FIELD THEORIES
UNIVERSE