# Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories

## TL;DR

This paper introduces a method to eliminate matter degrees of freedom in lattice gauge theories with staggered fermions by utilizing Gauss laws, resulting in extended interactions and modified local constraints.

## Contribution

The authors propose a novel approach to remove matter fields in lattice gauge theories, simplifying the Hamiltonian while managing the resulting changes in local interactions and constraints.

## Key findings

- Matter degrees of freedom can be fully removed using Gauss laws.
- The method introduces longer-range interactions and new local constraints.
- The approach applies to $U(N)$ and $SU(N)$ gauge theories.

## Abstract

Gauge theories, through the local symmetry which is in their core, exhibit many local constraints, that must be taken care of and addressed in any calculation. In the Hamiltonian picture this is phrased through the Gauss laws, local constraints that restrict the physical Hilbert space and relate the matter and gauge degrees of freedom. In this work, we present a way that uses all the Gauss laws in lattice gauge theories with staggered fermions for completely removing the matter degrees of freedom, at the cost of locally extending the interaction range, breaking the symmetry and introducing new local constraints, due to the finiteness of the original local matter spaces.