On Zero Energy States in SUSY Quantum Mechanics on Manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915149603930112 |
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| author | Avramidi, Ivan G. |
| author_facet | Avramidi, Ivan G. |
| contents | 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 $H_f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Zero Energy States in SUSY Quantum Mechanics on Manifolds Avramidi, Ivan G. Mathematical Physics High Energy Physics - Theory 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 $H_f$. |
| title | On Zero Energy States in SUSY Quantum Mechanics on Manifolds |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.09040 |