Trace and Index of Dirac-Schrödinger Operators on Open Space with Operator Potentials
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913610060529664 |
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| author | Fürst, Oliver |
| author_facet | Fürst, Oliver |
| contents | We develop a principal trace and generalized index formula for a Dirac-Schrödinger operator $D$ on open space of odd dimension $d\geq 3$ 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 $L^2\left(\mathbb{R}^{d+1},H\right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02593 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trace and Index of Dirac-Schrödinger Operators on Open Space with Operator Potentials Fürst, Oliver Functional Analysis Analysis of PDEs 47B10, 47A53, 47A55 (Primary), 47A10, 35P25, 81Q10 (Secondary) We develop a principal trace and generalized index formula for a Dirac-Schrödinger operator $D$ on open space of odd dimension $d\geq 3$ 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 $L^2\left(\mathbb{R}^{d+1},H\right)$. |
| title | Trace and Index of Dirac-Schrödinger Operators on Open Space with Operator Potentials |
| topic | Functional Analysis Analysis of PDEs 47B10, 47A53, 47A55 (Primary), 47A10, 35P25, 81Q10 (Secondary) |
| url | https://arxiv.org/abs/2311.02593 |