About renormalization of the Yang – Mills theory and the approach to calculation of the heat kernel
1 Department of Mathematics and Mathematical Physics, Physics Faculty of St. Petersburg State University
2 St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences 27 Fontanka, St. Petersburg, Russia
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Published online: 24 October 2017
The quantum theory of Yang – Mills in four-dimensional space – time plays an important role in modern theoretical physics. Currently, this model contains many open problems, therefore, it is of great interest to mathematicians. This work consists of several parts, however, it only offers a new approach and, therefore, it is methodological. First of all, the diagram technique and the mathematical basis will be recalled in the first part. Then the process of renormalization will be explained. It is based on momentum cut-off regularization and described in  and . However, this type of the regularization has several problems, as a result, only the first correction is calculated. After common constructions and observations, the first correction will be described in detail. Namely, the heat kernel will be considered since it plays a main role in this formalism. In particular, the method for calculating of coefficients of arbitrary order will be proposed.
© The authors, published by EDP Sciences, 2017
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