Quantum diffusion of magnetic fields in a numerical worldline approach

Abstract

We propose a numerical technique for calculating effective actions of electromagnetic backgrounds based on the worldline formalism. As a conceptually simple example, we consider scalar electrodynamics in three dimensions to one-loop order. Beyond the constant-magnetic-field case, serving as a benchmark test, we analyze the effective action of a step-function-like magnetic field -- a configuration that is inaccessible to derivative expansions. We observe magnetic-field diffusion, i.e., nonvanishing magnetic action density at space points near the magnetic step where the classical field vanishes.Comment: 15 pages, 3 figures, v2: numerical analysis in Sect.3 improved, references added, typos corrected, version to appear in NP