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arXiv · hep-th/9912003

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

Alan Carey·Jouko Mickelsson
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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.

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Alan Carey, Jouko Mickelsson. 2000-05-30. A gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundary. https://doi.org/10.1023/a%3A1007676919822

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