Functional integration measure in quantum gravity

Details Functional integration measure in quantum gravity Functional integration measure in quantum gravity

Jun 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..45.4473a&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 45, Issue 12, 15 June 1992, pp.4473-4485

Physics

10

Scientific paper

We study a peculiar regularization of quantum gravity at one-loop order intended to exhibit the properties of the functional measure. It reminds one of the Pauli-Villars technique in the sense that massive fields are introduced as regulators (and the mass is intended to go to infinity). The Pauli-Villars regulators are spin-2, -1, -1/2, and -0 particles coupled to gravity in a covariant way (mass terms included). We show that, under these conditions, the measure required in order to remove the maximal ultraviolet divergences [i.e., the divergences proportional to δ(r)(0) if r is the space-time dimension] is a product of measures of Fujikawa. Both the action and the measure of the functional integral are Becchi-Rouet-Stora (BRS) invariant. We consider also the regularization in the background-field formalism. We show that the measure of Fujikawa must be naturally generalized in order to be invariant under reparametrizations of the background as well as BRS invariant.

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