STRONG-COUPLING REGIME IN $g\phi^4_2$ THEORY

Abstract

The problem of the strong-coupling regime is considered in the scalar superrenormalizable field theory [Formula: see text]. By using the Gaussian transform, we have found an optimal representation within which the exact strong-coupling behavior of the free energy is already obtained in the leading-order approximation. Within this representation, the interaction becomes slower as the bare coupling constant grows, so the higher-order corrections can be systematically estimated by using a modified perturbation scheme. The next-to-leading terms give rise in insignificant corrections for finite coupling. The regularization procedure regroups the initial counterterms so that the divergencies are exactly removed in final expressions. The main idea is demonstrated in the simplest examples of a plain quartic integral and the anharmonic oscillator.