Spectral functions of the Dirac operator under local boundary conditions

Abstract

After a brief discussion of elliptic boundary problems and their properties, we concentrate on a particular example: the Euclidean Dirac operator in two dimensions, with its domain determined by local boundary conditions. We discuss the meromorphic structure of the zeta function of the associated second order problem, as well as the main characteristic of the first order problem, i.e., the boundary contribution to the spectral asymmetry, as defined through the eta function.