2002
DOI: 10.1016/s0550-3213(02)00835-0
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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 condensa… Show more

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Cited by 40 publications
(64 citation statements)
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“…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.…”
Section: Resultsmentioning
confidence: 73%
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“…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.…”
Section: Resultsmentioning
confidence: 73%
“…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),…”
Section: Worldline Discretizationmentioning
confidence: 99%
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“…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).…”
Section: The Photon Polarization Tensor For Inhomogeneous Fieldsmentioning
confidence: 99%