Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude
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.
Keywords
Cite
@article{arxiv.1802.08050,
title = {Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude},
author = {U. Camara da Silva},
journal= {arXiv preprint arXiv:1802.08050},
year = {2018}
}
Comments
23 pages; 6 figures