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Decomposition of the Twisted Dirac Operator

Tim Raeymaekers (UGent)
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Abstract
The classical Dirac operator is a conformally invariant first order differential operator mapping spinor-valued functions to the same space, where the spinor space is to be interpreted as an irreducible representation of the spin group. In this article we twist the Dirac operator by replacing the spinor space with an arbitrary irreducible representation of the spin group. In this way, the operator becomes highly reducible, whence we determine its full decomposition.
Keywords
Dirac operator, Higher spin, Clifford analysis

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Citation

Please use this url to cite or link to this publication:

Chicago
Raeymaekers, Tim. 2018. “Decomposition of the Twisted Dirac Operator.” In Clifford Analysis and Related Topics, ed. Paula Cerejeiras, Craig A. Nolder, John Ryan, and Carmen Judith Vanegas Espinoza. Springer.
APA
Raeymaekers, Tim. (2018). Decomposition of the Twisted Dirac Operator. In Paula Cerejeiras, C. A. Nolder, J. Ryan, & C. J. Vanegas Espinoza (Eds.), Clifford Analysis and Related Topics. Presented at the CART 2014, Springer.
Vancouver
1.
Raeymaekers T. Decomposition of the Twisted Dirac Operator. In: Cerejeiras P, Nolder CA, Ryan J, Vanegas Espinoza CJ, editors. Clifford Analysis and Related Topics. Springer; 2018.
MLA
Raeymaekers, Tim. “Decomposition of the Twisted Dirac Operator.” Clifford Analysis and Related Topics. Ed. Paula Cerejeiras et al. Springer, 2018. Print.
@inproceedings{8573607,
  abstract     = {The classical Dirac operator is a conformally invariant first order differential operator mapping spinor-valued functions to the same space, where the spinor space is to be interpreted as an irreducible representation of the spin group. In this article we twist the Dirac operator by replacing the spinor space with an arbitrary irreducible representation of the spin group. In this way, the operator becomes highly reducible, whence we determine its full decomposition.},
  author       = {Raeymaekers, Tim},
  booktitle    = {Clifford Analysis and Related Topics},
  editor       = {Cerejeiras, Paula and Nolder, Craig A. and Ryan, John and Vanegas Espinoza, Carmen Judith},
  isbn         = {978-3-030-00047-9},
  issn         = {2194-1009},
  keyword      = {Dirac operator,Higher spin,Clifford analysis},
  language     = {eng},
  location     = {Tallahassee, Florida},
  publisher    = {Springer},
  title        = {Decomposition of the Twisted Dirac Operator},
  url          = {http://dx.doi.org/10.1007/978-3-030-00049-3},
  year         = {2018},
}

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