Fermionic edge states and new physics
arXiv:1506.05243 · doi:10.1103/PhysRevD.92.045040
Abstract
We investigate the properties of the Dirac operator on manifolds with boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given. We show that the problem with the above boundary condition can be mapped to one where the manifold is extended beyond the boundary and the boundary condition is replaced by a delta function potential of suitable strength. We also briefly highlight how the problem of the self-adjointness of the operators in the presence of moving boundaries can be simplified by suitable transformations which render the boundary fixed and modify the Hamiltonian and the boundary condition to reflect the effect of moving boundary.
24 pages, 3 figures. Title changed, additional material in the Introduction section, the Application section and in the Discussion section highlighting some recent work on singular potentials, several references added. Conclusions remain unchanged. Version matches the version to appear in PRD
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