Euclidean quantum field theory and the Hawking effect
- 15 May 1978
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 17 (10), 2556-2566
- https://doi.org/10.1103/physrevd.17.2556
Abstract
Complex analytic continuation in a time variable in order to define a Feynman propagator is investigated in a general relativistic context. When external electric fields are present a complex analytic continuation in the electric charge is also introduced. The new Euclidean formalism is checked by reproducing Schwinger's special relativistic result for pair creation by an external, homogenous, electric field, and then applied to the Robinson-Bertotti universe. The Robinson-Bertotti universe, although unphysical, provides an interesting theoretical laboratory in which to investigate quantum effects, much as the unphysical Taub-NUT (Newman-Unti-Tamburino) universe does for purely classical general relativity. A conformally related problem of pair creation by a supercritically charged nucleus is also considered, and a sensible resolution is obtained to this classic problem. The essential mathematical point throughout is the use of the Feynman path-integral form of the propagator to motivate replacing hyperbolic equations by elliptic equations. The unique, bounded solution for the elliptic Green's function is then analytically continued back to physical values to define the Feynman Green's function.Keywords
This publication has 6 references indexed in Scilit:
- Cosmological event horizons, thermodynamics, and particle creationPhysical Review D, 1977
- Thermal particle production in two Taub-Nut type spacetimesCommunications in Mathematical Physics, 1976
- Path-integral derivation of black-hole radiancePhysical Review D, 1976
- Particle creation by black holesCommunications in Mathematical Physics, 1975
- Uniform Electromagnetic Field in the Theory of General RelativityPhysical Review B, 1959
- On Gauge Invariance and Vacuum PolarizationPhysical Review B, 1951