Summation of power singularities

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.

LaTeX, 8 pages. Firstly appeared in Russian, August 21, 2025, see https://www.pdmi.ras.ru/preprint/2025/25-10.html

References in corpus (11)

• Operator Cutoff Regularization and Renormalization Group in Yang-Mills Theory
• Three-Loop Yang-Mills beta-Function via the Covariant Background Field Method
• Summing Inflationary Logarithms in Nonlinear Sigma Models
• Explicit Cutoff Regularization in Coordinate Representation
• Scenario for the renormalization in the 4D Yang-Mills theory
• On Two-Loop Effective Action of 2D Sigma Model
• Radiative Corrections, Divergences, Regularization, Renormalization, Renormalization Group and All That in Examples in Quantum Field Theory
• Exact summation of leading infrared logarithms in 2D effective field theories
• Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions
• On a criterion for a cutoff regularization in the coordinate representation
• Exact expressions for the renormalization constants in the MS-like schemes