# Gauss law at a vertex in Lattice QCD and its gauge invariant Hilbert space

## TL;DR

This paper develops a method to solve the local Gauss law in lattice QCD with matter charges, constructing gauge-invariant states using Schwinger Bosons and Fermions, and analyzing operator actions for dynamics study.

## Contribution

It introduces a novel approach to construct gauge-invariant states in lattice QCD with matter charges using Schwinger Bosons and Fermions at each vertex.

## Key findings

- Constructed singlet states satisfying Gauss law with matter charges.
- Calculated the action of invariant operators on these states.
- Provided tools for studying dynamics in lattice QCD with matter.

## Abstract

We solve the local Gauss law in lattice QCD in the presence of matter charges. This corresponds to constructing singlet states using Schwinger Bosons and Fermions of SU(3) group at each vertex of the lattice. We also calculate the action of various invariant operators on these states required for studying the dynamics.