Smearing of propagators by gravitational fluctuations on the Planck scale

Details Smearing of propagators by gravitational fluctuations on the Planck scale Smearing of propagators by gravitational fluctuations on the Planck scale

Nov 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phrvd..60j4051o&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 60, Issue 10, 15 November 1999, id. 104051

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6

Covariant And Sum-Over-Histories Quantization, Quantum Field Theory In Curved Spacetime, Renormalization

Scientific paper

We examine the effects of quantum fluctuations in the gravitational field on the propagator of a spin-zero matter field. At short range, the propagator is a function of the square of the geodesic distance, and it can be expressed as an explicit functional of the gravitational field. Calculation of the path integral over the gravitational field is then possible, and this yields a gravitationally modified propagator. A renormalization of the gravitational constant is required, such that the bare gravitational constant approaches zero. To order G, the modified propagator is then -mK1(imx2-L2-iɛ)/4π2x2-L2-iɛ, where L~=Planck length. This result is consistent with the smeared propagator proposed in a previous paper, and it makes the radiative corrections in QED and in other field theories finite.

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