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

C. G. Beneventano·M. De Francia·E. M. Santangelo
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Abstract

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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C. G. Beneventano, M. De Francia, E. M. Santangelo. 1998-11-27. Dirac fields in a Bohm-Aharonov background and spectral boundary conditions. https://arxiv.org/abs/hep-th/9811242

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