Background field method

In theoretical physics, background field method is a useful procedure to calculate the effective action of a quantum field theory by expanding a quantum field around a classical "background" value B:

$A_{\mu }(x)=B_{\mu }(x)+a_{\mu }(x)$

After this is done, the Green's functions are evaluated as a function of the background. This approach has the advantage that the gauge invariance is manifestly preserved if the approach is applied to gauge theory.