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Translation of Harmonic Spinors and Interacting Weyl Fermions on Homogeneous Spaces

  • Salah Mehdi
  • N. Prudhon
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 207)

Abstract

We show that the image of the Poisson map, defined by Mehdi and Zierau in [9], which intertwines principal series representations with a submodule of the kernel of the cubic Dirac operator, commutes with the translation functor. As a byproduct, we obtain a systematic geometric process which produces interacting Weyl fermions with a fixed energy level on homogeneous spacetimes.

Keywords

Dirac operator Harmonic spinor Homogeneous space Admissible representation Translation functor Weyl fermion interaction 

2000 Mathematics Subject Classification

Primary 22E46 Secondary 22F30 22E70 

Notes

Acknowledgements

We thank the anonymous referee for his/her thorough review and highly appreciate the comments and suggestions, which significantly contributed to improving the text.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut Elie Cartan de LorraineUniversité de Lorraine, UMR CNRS7502MetzFrance

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