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

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

1995-06-14

arxiv.org/abs/hep-th/9506095v1

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, revtex, one figure included

Scientific paper

Pure Yang-Mills theories on the $S_1\times R$ cylinder are quantized in light-cone gauge $A_-=0$ by means of ${\bf equal-time}$ 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.

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