Dirac Quantization of the Chern-Simons Field Theory in the Coulomb Gauge

Details Dirac Quantization of the Chern-Simons Field Theory in the Coulomb Gauge Dirac Quantization of the Chern-Simons Field Theory in the Coulomb Gauge

1996-11-25

arxiv.org/abs/hep-th/9611211v1

Phys.Lett. B395 (1997) 250-256

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex+RevTex, no figures

Scientific paper

10.1016/S0370-2693(97)00023-3

In this letter the Chern-Simons field theories are studied in the Coulomb gauge using the Dirac's canonical formalism for constrained systems. As a strategy, we first work out the constraints and then quantize, replacing the Dirac brackets with quantum commutators. We find that the Chern-Simons field theories become two dimensional models with no propagation along the time direction. Moreover, we prove that, despite of the presence of non-trivial self-interactions in the gauge fixed functional, the commutation relations between the fields are trivial at any order in perturbation theory in the absence of couplings with matter fields. If these couplings are present, instead, the commutation relations become rather involved, but it is still possible to study their main properties and to show that they vanish at the tree level.

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