Pseudodifferential calculus in Schwinger--DeWitt formalism: UV and IR parts

Abstract

We consider expansions for the kernels of operator functions of second-order minimal operators on a curved background. We show that the terms of these expansions originate in the ultraviolet or infrared regions. We propose a systematic approach to obtaining ultraviolet terms using term-by-term integration of the DeWitt expansion of the heat kernel. We discuss two methods for regularizing infrared divergences arising at intermediate computational steps -- using analytic continuation and introducing a mass term -- and the relationship between them.

7 pages

References in corpus (5)

• Quantum Gravity at a Lifshitz Point
• Heat kernel expansion for higher order minimal and nonminimal operators
• Notes on peculiarities of Schwinger--DeWitt technique: one-loop double poles, total-derivative terms and determinant anomalies
• Schwinger--DeWitt expansion for the heat kernel of nonminimal operators in causal theories
• Functorial properties of Schwinger-DeWitt expansion and Mellin-Barnes representation