Semiclassical Methods in 2D QFT: Spectra and Finite-Size Effects

TL;DR

This paper reviews semiclassical techniques for analyzing two-dimensional quantum field theories with degenerate minima, focusing on spectra and finite-size effects, emphasizing their non-perturbative nature despite small coupling assumptions.

Contribution

It extends semiclassical methods to analyze non-perturbative spectra and finite-size effects in 2D QFTs with degenerate minima, building on classical techniques from the 1970s.

Findings

Semiclassical methods effectively analyze spectra in 2D QFTs.

The approach captures non-perturbative effects despite small coupling.

Finite-size effects can be controlled analytically using these techniques.

Abstract

We review some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques, which generalize methods introduced during the Seventies by Dashen, Hasllacher and Neveu and by Goldstone and Jackiw. The approach is best suited to deal with quantum field theories characterized by a non-linear interaction potential with different degenerate minima, that generates kink excitations of 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. We will discuss the efficacy of the semiclassical method as a tool to control analytically spectrum and finite-size effects in these theories.