V. V. Belokurov

CALCULATION OF LADDER DIAGRAMS IN ARBITRARY ORDER

A scalar ladder propagator-type diagram is rigorously calculated in an arbitrary order of perturbation theory.

NEW PERTURBATION THEORY FOR QUANTUM FIELD THEORY: CONVERGENT SERIES INSTEAD OF ASYMPTOTIC EXPANSIONS

Asymptotic expansions, employed in quantum physics as series of perturbation theory, appear as a result of the representation of functional integrals by power series with respect to coupling constant. To derive these series one has to change the order of functional integration and infinite summation. In general, this procedure is incorrect and is responsible for the divergence of the asymptotic expansions. In the present work, we suggest a method of construction of a new perturbation theory. In the framework of this perturbation theory, a convergent series corresponds to any physical quantity represented by a functional integral. The relations between the coefficients of these series and those of the asymptotic expansions are established.

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.

Perturbation Theory with Convergent Series for Arbitrary Values of Coupling Constant

In this letter, the method of the approximative calculation of functional integrals with any given accuracy1,2 is developed. Here we use the independence of the integrals on an auxiliary regularization parameter to simplify the calculations. Also we propose a modification of the method that proves to be more convenient for calculations with large values of coupling constants.

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.

New Perturbation Theory for Quantum Field Theory: Convergent Series Instead of Asymptotic Expansions

We present a new approach to perturbation theory for quantum field theory based on convergent series instead of asymptotic expansions. This approach could be considered as the next step after traditional perturbation theory calculations, which allows more comprehensive use of previously obtained information in finding numerical values with greater accuracy.

Exact solution of the Schwarzian theory

X iv :1 70 5. 02 40 5v 3 [ he pth ] 1 7 O ct 2 01 7 Exact solution of the Schwarzian theory Vladimir V. Belokurov Lomonosov Moscow State University, Leninskie gory 1, Moscow, 119991, Russia and Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow, 117312, Russia Evgeniy T. Shavgulidze Lomonosov Moscow State University, Leninskie gory 1, Moscow, 119991, Russia The explicit evaluation of the partition function in the Schwarzian theory is presented.

Convergent Perturbation Theory for the lattice

The standard lattice perturbation theory leads to the asymptotic series because of the incorrect interchange of the summation and integration. However, changing the initial approximation of the perturbation theory, one can generate the convergent series. We study the lattice

\phi^4

\phi^4

-model

-model and compare the operator