Solution of the confinement problem in 1D

Coupling matter to gauge fields can lead to confinement, which means that the original matter particles no longer exist as isolated excitations. The phenomenon is well known from quarks constituting baryons and mesons, but its origin remains poorly understood theoretically, especially when the matter fields are mobile.

In our recent paper, we solve the confinement problem with dynamical charges in one dimension by means of a non-local basis transformation. In the latter, the distances between particles are quantized rather than the fields themselves. We show that confinement corresponds to translational symmetry breaking in this string-length representation of the theory.