Is it possible to derive the chiral anomaly equation for the axial fermion current (in the form of an index theorem) by using only geometrical arguments, without introducing correlators, path integrals, Dirac seas etc.?
The chiral anomaly has the form of an index theorem, which has a topological origin. On the other hand, in the operator formalism it arises because of the absence of a chiral symmetry preserving regularization. I don't understand how these approaches are connected.