# Lattice Regularization of the Chiral Schwinger Model

## TL;DR

This paper investigates the lattice formulation of the chiral Schwinger model, proving positivity and existence of critical points, and analyzing the continuum limit of key physical quantities.

## Contribution

It establishes Osterwalder-Schrader positivity for certain lattice formulations and demonstrates the existence of critical points allowing continuum theory reconstruction.

## Key findings

- Proves positivity for non-compact and Wilson gauge formulations.
- Identifies critical points where continuum limit exists.
- Analytically controls the continuum limit of two-point functions.

## Abstract

We analyze the chiral Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. For non-compact and Wilson formulation of the gauge field action it is proven that the effective lattice model is Osterwalder-Schrader positive, which is a sufficient condition for the reconstruction of a physical Hilbert space from the model defined on a Euclidean lattice. For the non-compact model we furthermore establish the existence of critical points where the corresponding continuum theory can be reconstructed. We show that the continuum limit for the two-point functions of field strength and chiral densities can be controlled analytically. The article ends with some remarks on fermionic observables.