# Addition of SU(3) generators and its Singlet Hilbert space

## TL;DR

This paper constructs the singlet Hilbert space for SU(3) generators in lattice QCD, explicitly building basis states with Schwinger Bosons and analyzing operator actions to facilitate understanding of gauge invariance.

## Contribution

It introduces an explicit construction of the singlet Hilbert space for SU(3) using Schwinger Bosons, advancing the mathematical framework for lattice QCD.

## Key findings

- Explicit basis states for the singlet Hilbert space are constructed.
- The action of basic singlet operators on these states is computed.
- Provides a foundation for solving Gauss law in lattice QCD.

## Abstract

We construct the singlet Hilbert space associated with addition of SU(3) generators. This corresponds to the solution of Gauss law in lattice QCD. The normalized basis states are explicitly constructed using Schwinger Bosons. Further, we compute the action of basic singlet operators on these basis states.