Perturbative Analysis of Chern-simons Field Theory in the Coulomb Gauge

In this paper we analyse the perturbative aspects of Chern–Simons field theories in the Coulomb gauge. We show that in the perturbative expansion of the Green functions there are neither ultraviolet not infrared divergences. Moreover, all the radiative corrections are zero at any loop order. Some problems connected with the Coulomb gauge fixing, like the appearance of spurious singularities in the computation of the Feynman diagrams, are discussed and solved. The regularization used here for the spurious singularities can be easily applied also to the Yang–Mills case, which is affected by similar divergences. The work of F. Ferrari has been supported by the European Union, TMR Programme, under grant ERB4001GT951315 Laboratoire associé No. 280 au CNRS