Functional determinants for the Dirac equation with mixed pseudodifferential boundary conditions over finite cylinders

Abstract

In this note, we explicitly compute the functional determinant of a Dirac Laplacian with nonlocal pseudodifferential boundary conditions over a finite cylinder in terms of the ζ-function of the Dirac operator on the cross section and the pseudodifferential operators defining the boundary conditions. In particular, this result reduces to our previous formula [J. Phys. AJPHAC5 37, 7381 (2004)] for the special case of generalized Atiyah–Patodi–Singer conditions. To prove our main result, we use the gluing and comparison formulas established by the present authors in Refs 14 and 15.