One-loop effective action: nonlocal form factors and renormalization group

Understand

We review and present full detail of the Feynman diagram - based and heat-kernel method - based calculations of the simplest nonlocal form factors in the one-loop contributions of a massive scalar field.

• The paper has a pedagogical and introductory purposes and is intended to help the reader in better understanding the existing literature on the subject.
• The functional calculations are based on the solution by Avramidi and Barvinsky \& Vilkovisky for the heat kernel and are performed in curved spacetime.
• One of the important points is that the main structure of non-localities is the same as in the flat background.