Finite-volume effects and meson scattering in the 2-flavour Schwinger model

TL;DR

This paper studies finite-volume effects and meson scattering in the 2-flavour Schwinger model using canonical transfer matrices, providing insights into multi-particle energies and phase shifts in a lattice gauge theory context.

Contribution

It introduces a formalism with transfer matrices for analyzing multi-meson sectors and finite-volume effects in the 2-flavour Schwinger model, enabling direct computation of scattering properties.

Findings

Finite-volume effects on meson masses are characterized.

Meson scattering phase shifts are extracted from energy spectra.

Comparison with 3-particle quantization predictions shows consistency.

Abstract

We investigate the 2-flavour Schwinger model in the canonical formulation with fixed fermion numbers. We use Wilson fermions and a formalism which describes the determinant of the Dirac operator in terms of dimensionally reduced canonical transfer matrices. These transfer matrices allow the direct examination of arbitrary multi-particle (meson) sectors and the determination of the corresponding ground-state energies. We discuss the finite-volume effects in the meson mass. From the 2-meson energies, we determine the scattering phase shifts and compare the 3-meson energies at finite volume to predictions based on 3-particle quantization conditions.