Physical Account of Weyl Anomaly from Dirac Sea

TL;DR

This paper derives the Weyl anomaly in two-dimensional space-time by regularizing the Dirac sea with additional massive species, providing a novel perspective on anomaly calculation in quantum field theory.

Contribution

It introduces a new regularization method for the Dirac sea involving negatively counted massive species dependent on the gravitational background.

Findings

Derived the Weyl anomaly using the Dirac sea approach.

Established a regularization scheme with massive species.

Connected the anomaly to background gravitational fields.

Abstract

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