Summation of power singularities

TL;DR

This paper explores the summation of specific non-logarithmic singularities in a 2D non-linear sigma model, deriving an explicit formula that relates to the quantum action and introducing a new auxiliary function.

Contribution

It provides a novel explicit formula for summing certain singularities and introduces a new auxiliary function in the context of non-linear sigma models.

Findings

Derived an explicit formula for singularity summation

Reproduces part of the quantum action through formal expansion

Introduced and analyzed a new auxiliary function

Abstract

In this paper, we investigate an example of summation of non-logarithmic singularities of a specific type in a two-dimensional non-linear sigma model. As a result of the study, we obtained an explicit formula, which, upon formal expansion in terms of the coupling constant, reproduces a particular part of the quantum action. Additionally, the paper introduces a new auxiliary function and discusses some of its properties.