BORIS Theses

BORIS Theses
Bern Open Repository and Information System

The Schwinger model in the canonical formulation

Bühlmann, Patrick (2022). The Schwinger model in the canonical formulation. (Thesis). Universität Bern, Bern

22buehlmann_p.pdf - Thesis
Available under License Creative Commons: Attribution-Noncommercial-No Derivative Works (CC-BY-NC-ND 4.0).

Download (9MB) | Preview


We investigate the Schwinger model in the canonical formulation with fixed fermion numbers. For this, Wilson fermions and a formalism which describes the determinant of the Dirac operator in terms of dimensionally reduced canonical determinants are used. These canonical determinants are built from sums over principal minors of canonical transfer matrices. We consider the 1-flavour Schwinger model in a regime where the sign problem is absent and investigate several structural properties of the canonical determinants and their transfer matrices. Next, we discuss the 2-flavour Schwinger model in the canonical formulation. The transfer matrices allow the direct examination of arbitrary multi-particle (meson) sectors and the determination of the corresponding ground state energies. We determine the ground state energies and utilize them to perform some basic scattering theory and investigate finite volume effects in the meson mass. From the 2-meson energies the scattering phase shifts as a function of the volume were determined. Using a low-energy scattering theory, we describe the scattering process in terms of a few physical parameters. We use the scattering phase shifts to solve 3-particle quantization conditions which allow us to make predictions for the 3-meson energies at finite volume. These predictions are compared to direct measurements of the 3-meson energies.

Item Type: Thesis
Dissertation Type: Single
Date of Defense: 26 July 2022
Subjects: 500 Science > 530 Physics
Institute / Center: 08 Faculty of Science > Institute of Theoretical Physics
Depositing User: Hammer Igor
Date Deposited: 12 Aug 2022 12:35
Last Modified: 12 Aug 2022 12:43

Actions (login required)

View Item View Item