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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/179479We 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 unchangedHigh Energy Physics - TheoryA gerbe obstruction to quantization of fermions on odd dimensional manifolds with boundarytext