Loop-string-hadron approach to SU(3) lattice Yang-Mills theory, II: Operator representation for the trivalent vertex

TL;DR

This paper develops an operator representation for the trivalent vertex in the loop-string-hadron approach to SU(3) lattice Yang-Mills theory, enabling faster classical calculations and supporting quantum chromodynamics simulations.

Contribution

It introduces an infinite-dimensional matrix representation for gauge-invariant operators at a trivalent vertex, improving computational efficiency over previous Schwinger-boson methods.

Findings

Classical calculations in LSH basis are significantly faster.

Provides a standalone framework for operator computations.

Includes a companion code for practical implementation.

Abstract

This work is the second installment of a series on the loop-string-hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a trivalent vertex, which results in a standalone framework for computations that supersedes the underlying Schwinger-boson framework. To that end, we present a partial summary of the commutation relations and use it to evaluate the result of applying any gauge-invariant operator on the LSH basis states introduced in Part I (arXiv:2407.19181). Classical calculations in the LSH basis run significantly faster than equivalent calculations performed using Schwinger bosons. A companion code script is provided, which implements the derived formulas and aims to facilitate rapid progress towards Hamiltonian-based calculations of quantum chromodynamics.