A gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundary
High Energy Physics - Theory
2008-11-26 v3
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.
Keywords
Cite
@article{arxiv.hep-th/9912003,
title = {A gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundary},
author = {Alan Carey and Jouko Mickelsson},
journal= {arXiv preprint arXiv:hep-th/9912003},
year = {2008}
}
Comments
Improved introduction, minor corrections in the text, results unchanged