# The Lattice Schrodinger Functional and the Background Field Effective Action

## TL;DR

This paper introduces a novel lattice Schrödinger functional approach to study the effective action of background fields in lattice gauge theories, demonstrated through U(1) gauge theory with a magnetic field.

## Contribution

The paper presents a new method using the lattice Schrödinger functional to analyze background field effects in gauge theories, providing a practical computational framework.

## Key findings

- Method yields sensible results for U(1) gauge theory with magnetic field
- Demonstrates the effectiveness of the approach in a four-dimensional setting
- Provides a foundation for studying background fields in other gauge theories

## Abstract

We propose a new method that by using the lattice Schr\"odinger functional allows to investigate the effective action for external background fields in lattice gauge theories. We show that this method gives sensible results for the case of four-dimensional U(1) gauge theory in an external constant magnetic field.