Proof of summed form of proper-time expansion for propagator in curved space-time

Details Proof of summed form of proper-time expansion for propagator in curved space-time Proof of summed form of proper-time expansion for propagator in curved space-time

May 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..31.2439j&link_type=abstract

Physical Review D (Particles and Fields), Volume 31, Issue 10, 15 May 1985, pp.2439-2451

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73

Other Topics In Mathematical Methods In Physics, Theory Of Quantized Fields

Scientific paper

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.

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