We develop a principal trace and generalized index formula for a Dirac–Schrödinger operator D on open space of odd dimension d 3 with a potential given by a family of self-adjoint unbounded operators acting on an infinite-dimensional Hilbert space H. The presented results generalize formulas surrounding the Callias index theorem to the case of unbounded operator potentials, for which the operator D is not necessarily Fredholm. This is the principal novelty of this paper. As application, we include examples where the trace formula is used to calculate the Witten index of non-Fredholm massless (d+1) -Dirac–Schrödinger operators acting in L^2 (R^d+1, H).
Oliver Fürst (Wed,) studied this question.