Semiclassical methods in 2D QFT: spectra and finite-size effects

TL;DR

This thesis develops semiclassical techniques to analytically analyze the spectrum and finite-size effects in two-dimensional quantum field theories, applicable to both integrable and non-integrable systems with non-linear potentials.

Contribution

It introduces a generalized semiclassical method that does not require integrability, enabling analysis of a broad class of 2D quantum field theories with degenerate minima.

Findings

Analytical predictions for spectra and finite-size effects.

Applicable to non-integrable theories with non-linear potentials.

Non-perturbative results based on small coupling assumptions.

Abstract

In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies performed in the past years for conformally invariant and integrable theories, which have led to analytical predictions for several measurable quantities in the universality classes of statistical systems. Here we propose a semiclassical method to control analytically the spectrum and the finite-size effects in both integrable and non-integrable theories. The techniques used are appropriate generalizations of the ones introduced in seminal works during the Seventies by Dashen, Hasslacher and Neveu and by Goldstone and Jackiw. Their approaches, which do not require integrability and therefore can be applied to a large class of systems, are best suited to deal with those quantum field theories characterized by a non-linear interaction potential with different degenerate minima. In fact, these systems display kink excitations which generally have a large mass in the small coupling regime. Under these circumstances, although the results obtained are based on a small coupling assumption, they are nevertheless non-perturbative, since the kink backgrounds around which the semiclassical expansion is performed are non-perturbative too.