Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions

TL;DR

This paper introduces a novel regularization method for quantum scalar field actions on curved manifolds using an averaging operator, ensuring quasi-locality, consistency with manifold gluing, and compatibility with renormalization.

Contribution

It proposes a new averaging-based regularization technique that generalizes cutoff regularization for curved spaces and maintains consistency during manifold gluing and renormalization processes.

Findings

The regularization method is shown to be consistent with manifold gluing.

The approach extends to other models beyond scalar fields.

It is compatible with multiplicative renormalization.

Abstract

The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which leads to a quasi-locality and is a natural generalization of a cutoff regularization in the coordinate representation in the case of a curved metric. It is proved that the regularization method is consistent with a process of gluing of manifolds and partition functions, that is, with the transition from submanifolds to the main manifold using an additional functional integration. It is shown that the method extends to other models, and is also consistent with the process of multiplicative renormalization. Additionally, we discuss issues related to the correct introduction of regularization and the locality.