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Differential Regularization of Topologically Massive Yang-Mills Theory and Chern-Simons Theory

W. F. Chen·H. C. Lee·Z. Y. Zhu
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Abstract

We apply differential renormalization method to the study of three-dimensional topologically massive Yang-Mills and Chern-Simons theories. The method is especially suitable for such theories as it avoids the need for dimensional continuation of three-dimensional antisymmetric tensor and the Feynman rules for three-dimensional theories in coordinate space are relatively simple. The calculus involved is still lengthy but not as difficult as other existing methods of calculation. We compute one-loop propagators and vertices and derive the one-loop local effective action for topologically massive Yang-Mills theory. We then consider Chern-Simons field theory as the large mass limit of topologically massive Yang-Mills theory and show that this leads to the famous shift in the parameter $k$. Some useful formulas for the calculus of differential renormalization of three-dimensional field theories are given in an Appendix.

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W. F. Chen, H. C. Lee, Z. Y. Zhu. 1996-11-01. Differential Regularization of Topologically Massive Yang-Mills Theory and Chern-Simons Theory. https://doi.org/10.1103/physrevd.55.3664

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