Resummed effective action in the world-line formalism

Details Resummed effective action in the world-line formalism Resummed effective action in the world-line formalism

2003-06-25

arxiv.org/abs/hep-th/0306243v1

Nucl.Phys. B677 (2004) 430-450

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

Using the world-line method we resum the scalar one-loop effective action. This is based on an exact expression for the one-loop action obtained for a background potential and a Taylor expansion of the potential up to quadratic order in x-space. We thus reproduce results of Masso and Rota very economically. An alternative resummation scheme is suggested using ``center of mass'' based loops which is equivalent under the assumption of vanishing third and higher derivatives in the Taylor expansion but leads to simplified expressions. In an appendix some general issues concerning the relation between world-line integrals with fixed end points versus integrals with fixed center are clarified. We finally note that this method is also very valuable for gauge field effective actions where it is based on the Euler--Heisenberg type resummation.

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