Summary: We apply differential renormalization method in a study of three-dimensional topologically massive Yang-Mills theory, Chern-Simons theory and 3-dimensional QED. The method is especially suitable for such theories as it avoids the need for dimensional continuation of the three-dimensional antisymmetric tensor and its 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 the topologically massive Yang-Mills theory. We then consider the Chern-Simons field theory as the large mass limit of the topologically massive Yang-Mills theory, and show that this leads to the well-known shift in the parameter \(k\). Some useful formulas for the calculus of differential renormalization of three-dimensional field theories are given in the appendix.
For the entire collection see [Zbl 0944.00081].