Two-Loop Vacuum Diagrams in Background Field and Heisenberg-Euler Effective Action
Abstract
Description
We show that in arbitrary even dimension, the two-loop scalar QED Heisenberg-Euler effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, when the constant background field satisfies F^2 = -f^2 I, which in four dimensions coincides with the condition for self-duality, or definite helicity. This result relies on new recursion relations between two-loop and one-loop diagrams, with background field propagators. It also yields an explicit form of the renormalized two-loop effective action in a general constant background field in two dimensions.
16 pages; uses axodraw.sty; minor changes, corrected typos
16 pages; uses axodraw.sty; minor changes, corrected typos