Continuum and Lattice Coulomb-Gauge Hamiltonian

TL;DR

This paper reviews the canonical quantization of continuum Yang-Mills theory and derives both continuum and lattice Coulomb-gauge Hamiltonians using simplified methods, connecting continuum and lattice formulations.

Contribution

It introduces a simplified derivation of Coulomb-gauge Hamiltonians in both continuum and lattice Yang-Mills theories, bridging the two frameworks.

Findings

Derived continuum Coulomb-gauge Hamiltonian from Yang-Mills theory.

Established a simple method to obtain lattice Coulomb-gauge Hamiltonian from Kogut-Susskind Hamiltonian.

Connected continuum and lattice Coulomb gauges through explicit Hamiltonian derivations.

Abstract

We review the canonical quantization of continuum Yang-Mills theory, and derive the continuum Coulomb-gauge Hamiltonian by a simplification of the Christ-Lee method. We then analogously derive, by a simple and elementary method, the lattice Coulomb-gauge Hamiltonian in the minimal Coulomb gauge (and in other Coulomb gauges) from the known Kogut-Susskind Hamiltonian.