Chern-Simons Perturbation Theory

摘要: We study the perturbation theory for three dimensional Chern--Simons quantum field on a general compact manifold without boundary. show that after simple change of variables, action obtained by BRS gauge fixing in Lorentz has superspace formulation. The basic properties propagator and Feynman rules are written precise manner language differential forms. Using explicit description singularities, we prove is finite. Finally anomalous metric dependence $2$-loop partition function Riemannian (which was introduced to define fixing) can be cancelled local counterterm as $1$-loop case. In fact, equal connection, normalized precisely one would expect based framing Witten's exact solution.