New tests and applications of the worldline path integral in the first order formalism

Details New tests and applications of the worldline path integral in the first order formalism New tests and applications of the worldline path integral in the first order formalism

2005-11-02

arxiv.org/abs/hep-th/0511026v1

Phys.Rev. D73 (2006) 045010

Physics

High Energy Physics

High Energy Physics - Theory

26 pages

Scientific paper

10.1103/PhysRevD.73.045010

We present different non-perturbative calculations within the context of Migdal's representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar and Proca fields in the presence of constant electromagnetic fields, for an even-dimensional spacetime. Then we derive the propagator for a charged scalar field in a spacelike vortex (i.e., instanton) background, in a long-distance expansion, and the exact propagator for a massless Dirac field in 1+1 dimensions in an arbitrary background. Finally, we present an interpretation of the chiral anomaly in the present context, finding a condition that the paths must fulfil in order to have a non-vanishing anomaly.

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