Towards a Many-Body Treatment of Hamiltonian Lattice SU(N) Gauge Theory
N.E. Ligterink, N.R. Walet, and R.F. Bishop
TL;DR
This paper presents a novel Hamiltonian lattice gauge theory approach using the maximal-tree gauge, providing explicit solutions for multiple gauge groups and a scheme to construct eigenstates of the electric energy operator.
Contribution
It introduces a consistent framework for Hamiltonian lattice gauge theory with a complete variable set and a symbolic method for eigenstate construction, extending solutions to various SU(N) groups.
Findings
Explicit solutions for U(1), SU(2), SU(3), SU(4), and SU(5) gauge theories.
A scheme to construct eigenstates of the electric energy operator.
Mapping the one-plaquette problem onto an N-fermion problem.
Abstract
We develop a consistent approach to Hamiltonian lattice gauge theory, using the maximal-tree gauge. The various constraints are discussed and implemented. An independent and complete set of variables for the colourless sector is determined. A general scheme to construct the eigenstates of the electric energy operator using a symbolic method is described. It is shown how the one-plaquette problem can be mapped onto a N-fermion problem. Explicit solutions for U(1), SU(2), SU(3), SU(4), and SU(5) lattice gauge theory are shown.
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