(1+1)-Dimensional SU(N) Static Sources in E and A Representations

TL;DR

This paper investigates (1+1)-dimensional SU(N) Yang-Mills theory with static sources, constructing explicit wave functionals in the electric representation and analyzing their relation to Wilson lines, advancing understanding of gauge theories in low dimensions.

Contribution

It introduces a detailed construction of wave functionals in the electric representation for SU(N) Yang-Mills theory with static sources, linking A- and E-representations and providing explicit solutions.

Findings

Wave functionals are eigenstates of Gauss' law and Hamiltonian.

Fourier transformation connects Wilson lines to these solutions.

Explicit construction of solutions in the electric representation.

Abstract

Here is presented a detailed work on the (1+1) dimensional SU(N) Yang-Mills theory with static sources. By studying the structure of the SU(N) group and of the Gauss' law we construct in the electric representation the appropriate wave functionals, which are simultaneously eigenstates of the Gauss' operator and of the Hamiltonian. The Fourier transformation between the A- and the E-representations connecting the Wilson line and a superposition of our solutions is given.