The geometric $β$-function in curved space-time under operator regularization

Details The geometric $β$-function in curved space-time under operator regularization The geometric $β$-function in curved space-time under operator regularization

2009-09-23

arxiv.org/abs/0909.4122v2

Physics

Mathematical Physics

20 pages

Scientific paper

In this paper, I compare the generators of the renormalization group flow, or the geometric $\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\beta$-function for a scalar field theory on a closed compact Riemannian manifold is defined on the entire manifold. I then extend the analysis to find the generator of the renormalization group flow for a conformal scalar-field theories on the same manifolds. The geometric $\beta$-function in this case is not defined.

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