Analytic index and chiral fermions

A recent application of an index relation of the form, dim ker M - dim ker M† = υ, to the generation of chiral fermions in a vector-like gauge theory is reviewed. In this scheme the chiral structure arises from a mass term with a non-trivial index. The essence of the generalized Pauli-Villars regularization of chiral gauge theory, which is based on this mechanism, is also clarified. (author). 14 refs