Eigenvalue estimates for multi-form modified Dirac operators

Jan Gutowski; George Papadopoulos

doi:10.1016/j.geomphys.2020.103954

Eigenvalue estimates for multi-form modified Dirac operators

Jan Gutowski^*, George Papadopoulos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such estimates are presented for modified Dirac operators with a k-degree form 0≤k≤4, those modified with multi-degree (0,k)-form 0≤k≤3 and the horizon Dirac operators which are modified with a multi-degree (1,2,4)-form. In particular, we give the necessary geometric conditions for such operators to admit zero modes as well as those for the zero modes to be parallel with a respect to a suitable connection. We also demonstrate that manifolds which admit such parallel spinors are associated with twisted covariant form hierarchies which generalize the conformal Killing–Yano forms.

Original language	English
Article number	103954
Pages (from-to)	1-
Number of pages	24
Journal	JOURNAL OF GEOMETRY AND PHYSICS
Volume	160
Early online date	1 Oct 2020
DOIs	https://doi.org/10.1016/j.geomphys.2020.103954
Publication status	Published - Feb 2021

Keywords

Differential geometry
Dirac equation

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10.1016/j.geomphys.2020.103954

Eigenvalue estimates_GUTOWSKI_Accepted 23 Sep 2020_GOLD_VoRAccepted author manuscript, 492 KBLicence: CC BY-NC-ND

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N2 - We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such estimates are presented for modified Dirac operators with a k-degree form 0≤k≤4, those modified with multi-degree (0,k)-form 0≤k≤3 and the horizon Dirac operators which are modified with a multi-degree (1,2,4)-form. In particular, we give the necessary geometric conditions for such operators to admit zero modes as well as those for the zero modes to be parallel with a respect to a suitable connection. We also demonstrate that manifolds which admit such parallel spinors are associated with twisted covariant form hierarchies which generalize the conformal Killing–Yano forms.

AB - We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such estimates are presented for modified Dirac operators with a k-degree form 0≤k≤4, those modified with multi-degree (0,k)-form 0≤k≤3 and the horizon Dirac operators which are modified with a multi-degree (1,2,4)-form. In particular, we give the necessary geometric conditions for such operators to admit zero modes as well as those for the zero modes to be parallel with a respect to a suitable connection. We also demonstrate that manifolds which admit such parallel spinors are associated with twisted covariant form hierarchies which generalize the conformal Killing–Yano forms.

KW - Differential geometry

KW - Dirac equation

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Eigenvalue estimates for multi-form modified Dirac operators

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