# Vacuum State of Lattice Gauge Theory with Fermions in 2+1 Dimensions

## TL;DR

This paper compares two different vacuum states in 2+1 dimensional lattice gauge theory with fermions, showing that the Hermite form has a lower energy than the unitary form using variational methods.

## Contribution

It introduces a comparison between Hermite and unitary vacuum states in lattice gauge theory with fermions, demonstrating the Hermite vacuum's lower energy.

## Key findings

- Hermite vacuum has lower energy than the unitary vacuum.
- The Hermite vacuum is obtained in Hermite form for the fermion part.
- Variational method confirms the energy difference.

## Abstract

We investigate the vacuum state of the lattice gauge theory with fermions in 2+1 dimensions. The vacuum in the Hermite form for the fermion part is obtained; the vacuum in the unitary form has been proposed by Luo and Chen. It is shown that the Hermite vacuum has a lower energy than the unitary one through the variational method.