Wilson loops and light-cone gauge quantization on the space-time S1 x R cylinder.

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Yang-Mills theories on the {ital S}{sub 1}{times}{ital R} cylinder are quantized at equal time in the light-cone gauge {ital A}{sub {minus}}=0. Zero modes, related to the winding around the cylinder, provide topological variables with a nontrivial Hamiltonian. Positive and negative frequency components do contribute to Green functions, in particular, to the free propagator, in a causal way, leading to expressions different from the ones in the literature. They are tested in the calculation of a Wilson loop with lightlike sides: in the Abelian case it can be exactly computed, obtaining the expected exponentiation of the area; in the SU({ital N}) case the area exponentiation in terms of the Casimir constant of the fundamental representation is obtained only if a {open_quote}{open_quote}contact{close_quote}{close_quote} form of the propagator is used. If instead the causal propagator is adopted, only an {ital O}({ital g}{sup 4}) calculation has been obtained entailing also the presence of the Casimir constant of the adjoint representation. {copyright} {ital 1996 The American Physical Society.}