The background field method beyond one loop

Abstract

The background field approach to multi-loop calculations in gauge field theories is presented. A relation between the gauge-invariant effective action computed using this method and the effective action of the conventional functional approach is derived. Feynman rules are given and renormalization is discussed. It is shown that the renormalization programme can be carried out without any reference to fields appearing inside loops. Finally, as an explicit example, the two-loop contribution to the β function of pure Yang-Mills theory is calculated using the background field method.