Semiclassical Quantization

  • Walter Dittrich
  • Martin Reuter

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.

Keywords

Manifold 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Walter Dittrich
    • 1
  • Martin Reuter
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenFed. Rep. of Germany
  2. 2.Institut für Theoretische PhysikUniversität HannoverHannover 1Fed. Rep. of Germany

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