The Witten Index of massless (d+1)-Dirac-Schrödinger Operators

2024/05/27 by Oliver Fürst, Fürst, Oliver · 1 citation
Mathematics · Physics and Astronomy · #35J46 (Secondary) #47A53 #47B10 (Primary) #47D06 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.17123

openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

Abstract

We calculate the Witten index of a class of (non-Fredholm) Dirac-Schrödinger operators over ℝ^d+1 for d≥ 3 odd, and thus generalize known results for the case d=1. For a concrete example of the potential, we give a more explicit index formula, showing that the Witten index assumes any real number on this class of operators.

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