Stochastic Quantization of Linearized Euclidean Gravity and No-Ghost Feynman Rules

Abstract

Stochastic quantization of linearized Euclidearn gravity is discussed. To avoid the difficulty caused by the bottomlessness of the Euclidean action of gravity, we propose to start from the Langevin equation supplemented with a conformal restoring force which will be set zero after all calculations are performed. Through the method, we show that gravity can also be quantized without introducing gauge fixing on the basis of stochastic quantization method. We also apply the method of stochastic gauge fixing to gravity. In this case, we can perform fictious time integrations trivially in all orders of perturbation, and summarize the result in the form of the Feynman rules which do not include th e Faddeev-Popov ghost.