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We present different non-perturbative calculations within the context ofMigdal's representation for the propagator and effective action of quantumparticles. We first calculate the exact propagators and effective actions forDirac, scalar and Proca fields in the presence of constant electromagneticfields, for an even-dimensional spacetime. Then we derive the propagator for acharged scalar field in a spacelike vortex (i.e., instanton) background, in along-distance expansion, and the exact propagator for a massless Dirac field in1+1 dimensions in an arbitrary background. Finally, we present aninterpretation of the chiral anomaly in the present context, finding acondition that the paths must fulfil in order to have a non-vanishing anomaly.Comment: 26 page

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