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Commuting symmetry operators for the Dirac equation

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If you have a question about this talk, please contact David Kubiznak.

The Dirac operator is an important tool in physics. The theory of conformal Killing-Yano (CKY) forms shows that the most general symmetry operator for the Dirac equation that is linear in derivatives can be written in terms of CKY forms. In this talk I will provide an introduction to the current state of the theory and discuss recent results. It is possible to generate new CKY forms in terms of “Killing-Yano brackets”, that are linked to Schauten-Nijenhus brackets, by imposing linearity constraints. One application of these ideas is given by Kerr-NUT-(A)dS space-times with a tower of CKY tensors. For these there is a set of mutually commuting operators that commute with the Dirac operator, underlying separability of various field equations in these geometries.

This talk is part of the DAMTP Friday GR Seminar series.

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