Dirac fields in a Bohm-Aharonov background and spectral boundary conditions

Details Dirac fields in a Bohm-Aharonov background and spectral boundary conditions Dirac fields in a Bohm-Aharonov background and spectral boundary conditions

1998-11-27

arxiv.org/abs/hep-th/9811242v1

Physics

High Energy Physics

High Energy Physics - Theory

To appear in Proceedings of "Fourth Workshop on Quantum Field Theory under the influence of External Conditions"

Scientific paper

We study the problem of a Dirac field in the background of an Aharonov-Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behaviour of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and discuss the vacuum fermionic number and Casimir energy.

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