Fermion-induced quantum action of vortex systems

Abstract

The quantum action generated by fermions which are minimally coupled to abelian vortex background fields is studied in D=2+1 and D=3+1 Euclidean dimensions. We present a detailed analysis of single- and binary-vortex configurations using the recently developed method of worldline numerics. The dependence of the fermion-induced quantum action on the fermion mass and the magnetic fluxes carried by the vortices is studied, and the binary-vortex interaction is computed. Additionally, we discuss the chiral condensate generated from a dilute gas of vortices in the intermediate fermion mass range for the case D=3+1. As a byproduct, our findings provide insight into the validity limits of the derivative expansion, which is the standard analytical approach to inhomogeneous backgrounds.Comment: 21 pages, 8 figure

Pair production in inhomogeneous fields

“…This averaged-field approximation can be trusted on the fewpercent level for spatial variations of the size of the Compton wavelength. We would like to emphasize that the small validity bound of the derivative expansion for the imaginary part of the effective action density is not related to the same observation for the real part, as discovered in [39]; the latter arises from a subtle interplay between nonlocal quantum contributions and local counterterms, whereas the imaginary part is not affected by renormalization counterterms. Furthermore, the derivative expansion for the real part of the integrated effective action works well even for Compton-scale variations [56], whereas it breaks down early for the imaginary part, as displayed in Fig.…”

“…The worldline numerical algorithm for the present problem partly resembles closely those developed in detail in [37,38,39,40,41], the essential steps of which we will recall in the following for completeness. As a first step, we introduce the unit loop y(t),…”

“…The algorithm presented here is an immediate generalization of the standard algorithm successfully used for the real part of the effective action [37,38,39,40,41]. For a constant field in four dimensions, Eq.…”

“…In the present work, we solve these problems by using the recently developed numerical worldline techniques [37,38,39,40,41] which are based on the string-inspired worldline formalism [42,43,44,45,46,47,48,49,50]. The important advantage compared to other approaches lies in the fact that worldline numerics can be formulated independently of any symmetry of the background.…”

Optical Probes of the Quantum Vacuum: The Photon Polarization Tensor in External Fields

“…As these formulas ultimately require to carry out a path integral, powerful Monte-Carlo algorithms [26][27] can be used to reliably extract quantitative information in rather general background fields. Whereas the general formalism can straightforwardly be extended to spinor QED 28 , we here confine ourselves to scalar QED (with spinless electrons).…”