Zero-energy eigenstates for the Dirac boundary problem

Abstract

As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of “box-quantization”: the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ5 symmetry, apart from the usual breaking due to zero modes. We point out the relevance of this approach to the computation of instanton determinants and other problems involving Dirac spinors.