Semiclassical Quantization

Abstract

We want to investigate the semiclassical or one-loop approximation of our Chern-Simons model:

$$ S\;{S_0}\;{\rm{ + }}\;{S_{CS}}\;{\rm{,}} $$

(25.1)

where

$$ {S_0}[\eta ,\;A]\;{\rm{ = }}\;\int_0^T {dt} \left[ {\frac{1}{2}{\eta ^a}{\omega _{ab}}{{\dot \eta }^b} - H(\eta ) - \sum\limits_i {{A_i}} (t){J_i}(\eta (t))} \right] $$

$$ {S_{CS}}[A]\;{\rm{ = }}\;\int_0^T {dt} \sum\limits_i {{k_i}} {A_i}(t) $$

(25.2)

and k _i is fixed. We shall see that consistency requires k _i to assume (half-) integer values only. In the following, all fields are defined on [0, T] and are assumed to be periodic.