Vacuum Integration: UV- and IR-divergencies

TL;DR

This paper discusses the detailed techniques for massless vacuum integrations, emphasizing the use of sequential approaches to handle UV and IR divergences, with practical applications in effective potential calculations.

Contribution

It provides detailed insights into vacuum integration methods, especially the use of sequential approaches for singular distributions, which are not extensively covered in existing literature.

Findings

Clarifies the role of delta-functions in UV and IR regimes

Introduces a sequential approach to handle singular distributions

Enhances practical methods for effective potential calculations

Abstract

In this note we present the important details regarding the massless vacuum integrations which are not outlined in the literature. In particular, it has been shown how the delta-function represents either UV-regime or IR-regime. In the case of vacuum integration, we advocate the use of sequential approach to the singular generated functions (distributions). The sequential approach is extremely useful for many practical applications, in particular, in the effective potential method.