On Zero Energy States in SUSY Quantum Mechanics on Manifolds

2025/02/13 by Ivan G. Avramidi, Avramidi, Ivan G.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2502.09040

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the zero modes of the operator H_f=D^*_fD_f, with a Dirac type operator D_f, acting on the spinor bundle over a closed even dimensional Riemannian manifold M. The operator D_f=D+ifI is a deformation of the Dirac operator D by a smooth function f. We obtain sufficient conditions on the deformation function that guarantee the positivity of the operator H_f, that is, the absence of zero modes. We also show that these conditions are not necessary and provide an explicit counterexample of a zero mode of the operator H_f.

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