# Lattice Background Effective Action: a Proposal

## TL;DR

This paper introduces a new method using the Schr"odinger functional to compute gauge invariant effective actions for external backgrounds on the lattice, validated through U(1) gauge theory with magnetic fields.

## Contribution

It proposes a novel approach for calculating lattice gauge invariant effective actions, enhancing the analysis of background fields in lattice gauge theories.

## Key findings

- Method successfully computes effective actions in lattice gauge theories.
- Validated approach with U(1) gauge theory and magnetic background.
- Provides a new tool for studying external fields in lattice simulations.

## Abstract

We propose a method based on the Schr\"odinger functional for computing on the lattice the gauge invariant effective action for external background fields. We check this method by studying the U(1) lattice gauge theory in presence of a constant magnetic background field.