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Quantum diffusion of magnetic fields in a numerical worldline approach
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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.
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Propagator from Nonperturbative Worldline Dynamics
Worldline Monte Carlo with a fitted potential PDF gives an all-orders quenched propagator for S2QED, with a pole mass that drops toward zero near a critical coupling around 0.72.
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