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We develop trace and index formulas for a Dirac-Schr\"odinger operator onopen space of dimension $d\geq 3$ with a potential given by a family ofself-adjoint unbounded operators acting on a infinite dimensional Hilbert space$H$. The index formula generalizes the Callias Index Theorem to unboundedoperators, while the trace formula generalizes existing trace formulas of $d=1$to higher dimensions.

Trace and Index of Dirac-Schr\"odinger Operators on Open Space with Operator Potentials