# Laplacian Abelian Projection

## TL;DR

The paper introduces a new gauge fixing method for abelian projection using the lowest eigenvector of a covariant Laplacian, ensuring smoothness and eliminating lattice Gribov copies for clearer gauge field analysis.

## Contribution

It proposes a novel partial gauge fixing condition based on the covariant Laplacian eigenvector, improving gauge field computations.

## Key findings

- Gauge is smooth and free of lattice Gribov copies
- Enables unambiguous abelian projected gauge field configuration
- Improves accuracy of gauge fixing in lattice simulations

## Abstract

A new partial gauge fixing condition for the abelian projection is introduced. It is based on the lowest-lying eigenvector of a covariant Laplacian operator. This gauge is smooth and free of lattice Gribov copies. These properties are important for an unambiguous computation of the abelian projected gauge field configuration.