The stress tensor conformal anomaly and analytic regularizations

Abstract

In this paper the stress tensor conformal anomaly of a conformally coupled scalar field defined in a d dimensional Riemannian manifold is derived with or without a boundary, using the zeta function analytic regularization method. It is found that the scalar anomaly is independent of any massless limit. In an odd dimensional manifold with a boundary, the anomaly is not zero owing the boundary condition dependent term. After briefly discussing the cutoff method, it is proven that the zeta function method is equivalent to the cutoff method with a subtraction of the polar terms.