Geometric quantization of topological gauge theories

Abstract

We study the symplectic quantization of Abelian gauge theories in 2 + 1 space-time dimensions with the introduction of a topological Chern-Simons term.

Faddeev-Jackiw Formalism for a Topological-Like Oscillator in Planar Dimensions

“…while the others are vanishing. The last three of the above Dirac brackects coincide with those given by Barcelos-Neto and de Souza [17] for the pure Chern-Simons theory, in the A 0 = 0 gauge. The first three relations can be rewritten in terms of the canonical momentum of the particle, as was done for the simple oscillator in previous section:…”

“…Therefore, following ref. [17], we are going to fix the gauge, which we choose to be the Weyl one (A 0 = 0). Once A 0 is absent from the Lagrangian (3.15) and noting the equivalence A 0 =λ we introduce a Lagrange multiplier η = η( x) for λ: (3.20) so that the new coefficients are given by a…”

“…In order to apply the symplectic formalism we should first linearize the quadratic term q2 . Following the procedure adopted in a recent paper [17], we have q2 −→ 2p. q − p 2 .…”