# The Coupled Cluster Method in Hamiltonian Lattice Field Theory

## TL;DR

This paper develops a new coupled cluster method for lattice Hamiltonian QCD that simplifies calculations by using character functions and group theory, enabling analysis of eigenstates with arbitrary momentum and angular momentum.

## Contribution

It introduces a novel construction for coupled cluster matrix elements in lattice QCD, avoiding gauge group coefficients and simplifying the eigenvalue problem setup.

## Key findings

- New prescription for coupled cluster matrix elements
- Method to handle arbitrary lattice momentum and angular momentum
- Simplified eigenvalue problem formulation

## Abstract

The coupled cluster or exp S form of the eigenvalue problem for lattice Hamiltonian QCD (without quarks) is investigated. A new construction prescription is given for the calculation of the relevant coupled cluster matrix elements with respect to an orthogonal and independent loop space basis. The method avoids the explicit introduction of gauge group coupling coefficients by mapping the eigenvalue problem onto a suitable set of character functions, which allows a simplified procedure. Using appropriate group theoretical methods, we show that it is possible to set up the eigenvalue problem for eigenstates having arbitrary lattice momentum and lattice angular momentum.