Yang-Mills theories on the S1×R cylinder are quantized at equal time in the light-cone gauge A-=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(N) case the area exponentiation in terms of the Casimir constant of the fundamental representation is obtained only if a "contact form of the propagator is used. If instead the causal propagator is adopted, only an O(g4) calculation has been obtained entailing also the presence of the Casimir constant of the adjoint representation

Nardelli, G., Bassetto, A., Griguolo, L., Wilson loops and light cone gauge quantization on the space-time S(1) x R cylinder, <<PHYSICAL REVIEW D>>, 1996; 1996 (54): 2845-2852. [doi:10.1103/PhysRevD.54.2845] [http://hdl.handle.net/10807/8561]

Wilson loops and light cone gauge quantization on the space-time S(1) x R cylinder

Nardelli, Giuseppe;Bassetto, Antonio;
1996

Abstract

Yang-Mills theories on the S1×R cylinder are quantized at equal time in the light-cone gauge A-=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(N) case the area exponentiation in terms of the Casimir constant of the fundamental representation is obtained only if a "contact form of the propagator is used. If instead the causal propagator is adopted, only an O(g4) calculation has been obtained entailing also the presence of the Casimir constant of the adjoint representation
Inglese
Nardelli, G., Bassetto, A., Griguolo, L., Wilson loops and light cone gauge quantization on the space-time S(1) x R cylinder, <<PHYSICAL REVIEW D>>, 1996; 1996 (54): 2845-2852. [doi:10.1103/PhysRevD.54.2845] [http://hdl.handle.net/10807/8561]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/8561
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