Abstract
We consider the canonical quantization of fermions on an odd-dimensional manifold with boundary, with respect to a family of elliptic Hermitian boundary conditions for the Dirac Hamiltonian. We show that there is a topological obstruction to a smooth quantization as a function of the boundary conditions. The obstruction is given in terms of a gerbe and its Dixmier–Douady class is evaluated.
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Carey, A., Mickelsson, J. A Gerbe Obstruction to Quantization of Fermions on Odd-Dimensional Manifolds with Boundary. Letters in Mathematical Physics 51, 145–160 (2000). https://doi.org/10.1023/A:1007676919822
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DOI: https://doi.org/10.1023/A:1007676919822