A gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundary

Abstract

We consider the canonical quantization of fermions on an odd dimensional manifold with boundary, with respect to a family of elliptic hermitean 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.

Improved introduction, minor corrections in the text, results unchanged

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