Hamiltonian formulation of Wilson's lattice gauge theories

TLDR

Wilson’s lattice gauge theory is formulated as a canonical Hamiltonian system of infinitely many coupled rigid rotators, whose gauge‑invariant configuration space consists of non‑Abelian electric flux strings terminating on quarks, a picture that is especially natural in the strong‑coupling limit. Quark confinement follows from the fact that a string cannot be broken without creating a quark–antiquark pair.

Abstract

Wilson's lattice gauge model is presented as a canonical Hamiltonian theory. The structure of the model is reduced to the interactions of an infinite collection of coupled rigid rotators. The gauge-invariant configuration space consists of a collection of strings with quarks at their ends. The strings are lines of non-Abelian electric flux. In the strong-coupling limit the dynamics is best described in terms of these strings. Quark confinement is a result of the inability to break a string without producing a pair.