Fermionic zero modes in the vortex field in arbitrary dimensions and index of Dirac operator with Majorana-like interaction
High Energy Physics - Theory
2013-05-30 v2
Abstract
In this work we consider fermionic zero modes in the external scalar and electromagnetic field forming the vortex on a sphere. We find the correspondence between the equations for the fermions in different dimensions, find their explicit expressions through the vortex fields in case of massless fermions, asymptotics near the poles in case of massive fermions and check the number of the solutions by proving index theorem for the fermions on a sphere. As a part of deriving the index, we write a detailed calculation of the Green function of the Heat equation.
Keywords
Cite
@article{arxiv.1110.6911,
title = {Fermionic zero modes in the vortex field in arbitrary dimensions and index of Dirac operator with Majorana-like interaction},
author = {Grigory Bednik},
journal= {arXiv preprint arXiv:1110.6911},
year = {2013}
}
Comments
30 pages