Renormalization of the quantum equation of motion for Yang–Mills fields in background formalism

The aim of this work is to compare renormalizations of the infinite parts of the Effective Action and Quantum Equation of Motion in gauge fields theory with $SU(N)$ as a structural group in the One-Loop Approach and to make sure that they do not coincide. To this end, we use the Background Formalism, in which a gauge field is decomposed into the sum of a classical (background) and a quantum field: $A=B+gQ$. The appearance of an additional factor, which provides the recovery of the equality of renormalizations of Equations and Action, is explained with the help of comparison with results of the standard renormalization theory of Yang–Mills fields.