New approach to summation of field-theoretical series in models with strong coupling

TL;DR

The paper introduces a novel summation method for divergent field-theoretical series using Borel transformation and conformal mapping, applicable to quantum mechanics and conformal field models, without requiring asymptotic parameters.

Contribution

It presents a new summation technique combining Borel transform and conformal mapping that does not need asymptotic data, enhancing calculations in strongly coupled field theories.

Findings

Successfully tested on asymptotic power series functions

Estimated ground state energies in quantum mechanical problems

Calculated critical exponents in conformal field models

Abstract

A new approach to summation of divergent field-theoretical series is suggested. It is based on the Borel transformation combined with a conformal mapping and does not imply the knowledge of the exact asymptotic parameters. The method is tested on functions expanded in their asymptotic power series and applied to estimating the ground state energy of simple quantum mechanical problems including anisotropic oscillators and caclulating the critical exponents for certain comformal field models. It can be expected that the new approach to summation may be used to obtaining numerical estimates for important physical quantities represented by divergent series in two- and three-dimensional field models.