Physical account of Weyl anomaly from Dirac Sea

Abstract

We rederive in a physical manner the Weyl anomaly in two-dimensional space–time by considering the Dirac Sea. It is regularized by some bosonic extra species which are formally negatively counted. In fact, we calculate the trace of the energy–momentum tensor in the Dirac Sea in presence of background gravitational field. It has to be regularized, since the Dirac Sea is bottomless and thus causes divergence. The new regularization method consists in adding various massive bosonic species some of which are to be counted negative in the Dirac Sea. The mass terms in the Lagrangian of the regularization fields have a dependence on the background gravitational field.