Grassmanian and chiral anomaly

Abstract

We discuss the Grassmanian of self-adjoint global elliptic boundary conditions with γ 5- and gauge-invariance of the domain for the Dirac operator over the 4-ball coupled to a gauge configuration with non-trivial curvature form. We show that this space contains a variety of boundary conditions in addition to the spectral Atiyah-Patodi-Singer projection and that some of them, like the Calderón projector, imply the vanishing of the index of the Dirac operator and therefore the invariance of the fermion determinant under global (i.e. rigid) chiral transformations.