Proof of summed form of proper-time expansion for propagator in curved space-time
Abstract
We consider the Schwinger-DeWitt proper-time expansion of the kernel of the Feynman propagator in curved space-time. We prove that the proper-time expansion can be written in a new form, conjectured by Parker and Toms, in which all the terms containing the scalar curvature R are generated by a simple overall exponential factor. This sums all terms containing R, including those with nonconstant coefficients, in the proper-time series. This result is valid for an arbitrary space-time and for any spin. It also applies to the heat kernel. This form of the expansion is of importance in connection with nonperturbative effects in quantum field theory.
- Authors:
- Publication Date:
- Research Org.:
- Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
- OSTI Identifier:
- 5859458
- Resource Type:
- Journal Article
- Journal Name:
- Phys. Rev. D; (United States)
- Additional Journal Information:
- Journal Volume: 31:10
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; PROPAGATOR; SPACE-TIME; BOUNDARY CONDITIONS; GREEN FUNCTION; SCALAR FIELDS; SCHROEDINGER EQUATION; SPIN; YANG-MILLS THEORY; ANGULAR MOMENTUM; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE PROPERTIES; WAVE EQUATIONS; 645400* - High Energy Physics- Field Theory
Citation Formats
Jack, I, and Parker, L. Proof of summed form of proper-time expansion for propagator in curved space-time. United States: N. p., 1985.
Web. doi:10.1103/PhysRevD.31.2439.
Jack, I, & Parker, L. Proof of summed form of proper-time expansion for propagator in curved space-time. United States. https://doi.org/10.1103/PhysRevD.31.2439
Jack, I, and Parker, L. 1985.
"Proof of summed form of proper-time expansion for propagator in curved space-time". United States. https://doi.org/10.1103/PhysRevD.31.2439.
@article{osti_5859458,
title = {Proof of summed form of proper-time expansion for propagator in curved space-time},
author = {Jack, I and Parker, L},
abstractNote = {We consider the Schwinger-DeWitt proper-time expansion of the kernel of the Feynman propagator in curved space-time. We prove that the proper-time expansion can be written in a new form, conjectured by Parker and Toms, in which all the terms containing the scalar curvature R are generated by a simple overall exponential factor. This sums all terms containing R, including those with nonconstant coefficients, in the proper-time series. This result is valid for an arbitrary space-time and for any spin. It also applies to the heat kernel. This form of the expansion is of importance in connection with nonperturbative effects in quantum field theory.},
doi = {10.1103/PhysRevD.31.2439},
url = {https://www.osti.gov/biblio/5859458},
journal = {Phys. Rev. D; (United States)},
number = ,
volume = 31:10,
place = {United States},
year = {Wed May 15 00:00:00 EDT 1985},
month = {Wed May 15 00:00:00 EDT 1985}
}
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