E. T. Shavgulidze

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.

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.

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.

Extraordinary properties of functional integrals and groups of diffeomorphisms

A review of the work of the authors is presented, in which corollaries of the quasi-invariance of functional integrals on the Wiener measure with respect to the action of a group of diffeomorphisms are studied, and the behavior of functional integrals with nonlinear nonlocal change of variables of integration is investigated as well. Using these substitutions, the functional integrals over discontinuous paths can be determined. The simplest models of the (Euclidean) quantum field theory are offered, in which the presence of hidden internal symmetries or the allowance for discontinuous paths in functional integrals leads to a number of paradoxical properties contradicting the conventional view.

Non-Hilbert spaces: a way to new physics?

We give some examples of the problems where non-Hilbert spaces could be relevant.