A gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundary
Abstract
Description
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
Improved introduction, minor corrections in the text, results unchanged