Exact Solution for the Most General Minimally Coupled One Dimensional Lattice Gauge Theory

TL;DR

This paper demonstrates that the most general one-dimensional lattice gauge theories with minimal coupling are exactly solvable in the thermodynamic limit, revealing no phase transitions and providing explicit solutions for special cases.

Contribution

It presents the first exact solutions for the broad class of minimally coupled one-dimensional lattice gauge theories, including special finite lattice cases.

Findings

Exact solvability in the thermodynamic limit

No phase transitions in these models

Explicit solutions for special finite lattice cases

Abstract

We consider one dimensional lattice gauge theories constructed by the minimal coupling prescription. It is shown that these theories are exactly solvable in the thermodynamic limit. After considering the most general case, we discuss some special cases on finite lattices, and also work out some examples. There is no phase transition in these minimally coupled theories.