Evgeni T. Shavgulidze

Method of approximate evaluation of path integrals using perturbation theory with convergent series. I

We propose a method of evaluating path integrals such that the integral is approximated with any accuracy by summations of a finite number of terms of an absolutely convergent series.

Method for approximate evaluation of path integrals using perturbation theory with convergent series. II. Euclidean quantum field theory

The proof is given of the method suggested in the previous paper for an approximate evaluation of path integrals in Hilbert space where the Gaussian measure is defined by a kernel operator.

Perturbation theory with convergent series for calculating physical quantities specified by finitely many terms of a divergent series in traditional perturbation theory

A new high-accuracy method is suggested for calculating physical quantities for which only finitely many terms of the divergent series in a traditional perturbation theory are known. The method is based on approximating the desired quantity with the sum of finitely many terms of an absolutely convergent series. As an example, the β-function in the ϕ44 model and the critical exponent α characterizing the behavior of the He4 heat capacity near the phase transition point are calculated.