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arXiv · 1802.08050

Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude

U. Camara da Silva
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Abstract

The Aharonov-Bohm elastic scattering with incident particles described by plane waves is revisited by using the phase-shifts method. The formal equivalence between the cylindrical Schr\"odinger equation and the one-dimensional Calogero problem allows us to show that up to two scattering phase-shifts modes in the cylindrical waves expansion must be renormalized. The renormalization procedure introduces new length scales giving rise to spontaneous breaking of the conformal symmetry. The new renormalized cross-section has an amazing property of being non-vanishing even for a quantized magnetic flux, coinciding with the case of Dirac delta function potential. The knowledge of the exact beta function permits us to describe the renormalization group flows within the two-parametric family of renormalized Aharonov-Bohm scattering amplitudes. Our analysis demonstrates that for quantized magnetic fluxes a BKT-like phase transition at the coupling space occurs.

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U. Camara da Silva. 2018-02-22. Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude. https://arxiv.org/abs/1802.08050

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