Renormalization of gauge theories without cohomology
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We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin–Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
KeywordsGauge Theory Gauge Symmetry Master Equation Classical Action Canonical Transformation
The investigation of this paper was carried out as part of a program to complete the book , which will be available at http://renormalization.com once completed. I thank the Perimeter Institute, Waterloo, Ontario, Canada, for hospitality during the first stage of this work and the Physics Department of Fudan University, Shanghai, for hospitality during the final stage of this work.