Please use this identifier to cite or link to this item: http://www.repositorio.ufop.br/handle/123456789/4936
Title: Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets.
Authors: Cariglia, Marco
Krtous, Pavel
Kubiznak, David
Issue Date: 2011
Citation: CARIGLIA, M.; KRTOUS, P.; KUBIZNAK, D. Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets. Physical Review. D, Particles, Fields, Gravitation, and Cosmology, v. 84, p. 024004, 2011. Disponível em: <http://journals.aps.org/prd/pdf/10.1103/PhysRevD.84.024004>. Acesso em: 23 fev. 2015.
Abstract: In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms, respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important nontrivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].
URI: http://www.repositorio.ufop.br/handle/123456789/4936
ISSN: 05562821
metadata.dc.rights.license: Permite o arquivamento da versão PDF do editor em repositórios institucionais. Fonte: Sherpa/Romeo <http://www.sherpa.ac.uk/romeo/search.php?issn=0556-2821>. Acesso em: 09 fev. 2015.
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