Celebratio Mathematica — Singer — Complete Bibliography

Complete Bibliography

Works connected to Scott Elliot Axelrod

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S. Axelrod and I. M. Singer: “Chern–Simons perturbation theory,” pp. 3–45 in Proceedings of the XXth international conference on differential geometric methods in theoretical physics (New York, 3–7 June 1991), vol. 1. Edited by S. Catto and A. Rocha. World Scientific (River Edge, NJ), 1992. MR 1225107 Zbl 0813.53051 ArXiv hep-th/9110056 incollection

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

Scott Elliot Axelrod	Related
Alvany Rocha-Caridi	Related
Sultan Catto	Related

S. Axelrod and I. M. Singer: “Chern–Simons perturbation theory, II,” J. Diff. Geom. 39 : 1 (1994), pp. 173–213. Also published in Perspectives in mathematical physics (1994). Part I was published in Proceedings of the XXth international conference on differential geometric methods in theoretical physics (1992). MR 1258919 Zbl 0827.53057 ArXiv hep-th/9304087 article