Trace and Index of Dirac-Schrödinger Operators on Open Space with Operator Potentials

2023/11/05 by Fürst, Oliver · 1 citation
#35P25 #47A10 #47A53 #47A55 (Primary) #47B10 #81Q10 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2311.02593

Abstract

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 a infinite dimensional Hilbert space H. The presented results generalize formulas surrounding the Callias index theorem to 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 L²(ℝ^d+1,H).

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