Callias-type operators associated to spectral triples
Callias-type (or Dirac-Schroedinger) operators associated to
abstract semifinite spectral triples are introduced and their indices
are computed in terms of an associated index pairing derived from the
spectral triple. The result is then interpreted as an index theorem for
a non-commutative analogue of spectral flow. Both even and odd spectral
triples are considered, and both commutative and non-commutative
examples are given.