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 delta(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.
FUNCTIONAL-INTEGRATION MEASURE IN QUANTUM-GRAVITY
ANSELMI, DAMIANO
1992-01-01
Abstract
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 delta(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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
