Quantization of Chern-Simons field theory in the Coulomb gauge

Abstract

We consider here the Chern-Simons field theory with gauge group SU(N) in the presence of a gravitational background that describes a two-dimensional expanding "universe".Two special cases are treated here in detail: the spatially flat Robertson-Walker space-time and the conformally static space-times having a general closed and orientable Riemann surface as spatial section. The propagator and the vertices are explicitely computed at the lowest order in perturbation theory imposing the Coulomb gauge fixing.

Dirac quantization of the Chern-Simons field theory in the Coulomb gauge

“…As it happens in the case of the more popular covariant gauges, also in this gauge the C-S functional contains self-interactions, but the Feynman rules simplify considerably and can be explicitly derived even on space-times with a non-flat spatial section [6]. Another advantage of the Coulomb gauge is that there are no time derivatives in the gauge fixed action, so that the C-S theory becomes in practice a two-dimensional model.…”

“…Another advantage of the Coulomb gauge is that there are no time derivatives in the gauge fixed action, so that the C-S theory becomes in practice a two-dimensional model. Despite of many physical and mathematical applications of the C-S field theories [3,7], however, until now only a few calculations have been performed in the Coulomb gauge [6,8,9]. One of the main reasons is that, already in the case of the Yang-Mills field theories, several perplexities arise concerning the use of this gauge [11][12][13].…”

“…On the other side, the ambiguities in the Yang-Mills Feynman integrals pointed out in [11] arise as well in the nonabelian C-S field theories due to the absence of time derivatives in the action [6]. A simple recipe to regularize such ambiguities has been proposed and successfully tested in first order calculations [6].…”

Non-perturbative particle dynamics in (2+1)-gravity

“…However, the method just outlined applies in general to N particles, provided we are able to solve the monodromies (13) by the auxiliary function f , transforming as in Eq. (15).…”

“…A key ingredient of the present solution is our choice of gauge [13]- [14], which is of conformal type and is also of Coulomb type [4]- [15] , i.e., it yields an instantaneous propagation.…”