Yang-Mills theories on the space-time $S_1\times R$ cylinder: equal-time quantization in light-cone gauge and Wilson loops

Abstract

Pure Yang-Mills theories on the $S_1\times R$ cylinder are quantized in light-cone gauge $A_{-}=0$ by means of $\mathbf{equal}-\mathbf{time}$ commutation relations. Positive and negative frequency components are excluded from the ``physical" Hilbert space by imposing Gauss' law in a weak sense. Zero modes, related to the winding on the cylinder, provide non trivial topological variables of the theory. A Wilson loop with light-like sides is studied: in the abelian case it can be exactly computed obtaining the expected area result, whereas difficulties are pointed out in non abelian cases.

21 pages, revtex, one figure included