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

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.Comment: 13 pages; uses axodraw.st

Quantum gauge field theory

Canonical quantization of a gauge theory in the spatial axial gauge produces an anisotropic Hamiltonian and matter particles surrounded by physically unrealistic asymmetric electric or chromoelectric fields. In the first part of my dissertation I show how to restore rotational symmetry for a nonabelian theory with a gauge fixing condition Aa3 = 0. I also discuss similarities between recovering isotropy in the spatial axial gauge and finding gauge invariant quantities in the Weyl gauge in both abelian and nonabelian field theories. ^ In the second part I further develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a background electromagnetic field. I show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general background field, which is a generalization of previously obtained results. For a constant background the fully renormalized effective action is found. No integrals need to 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. I also show that when the constant background field satisfies F 2 = –f21, which in four dimensions coincides with the condition for self-duality, or definite helicity, the two-loop effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, in arbitrary even dimensions. 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. Further I show how these diagrammatical rules can be applied to calculation of the three-loop effective action.