"Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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13 pages; uses axodraw.sty

Scientific paper

10.1088/1126-6708/2006/04/020

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.

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