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The Clifford Algebra of Physical Space and Elko Spinors

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Abstract

Elko spinors are eigenspinors of the charge conjugation operator. In this work we use the Clifford algebra of the physical space in order to formulate the theory of Elko spinors and use a procedure analog to Ryder’s derivation of Dirac equation to come up with an equation for Elko spinor fields. Unlike other works in the literature where an equation for Elko spinor fields has been studied, in this work we obtain a first order differential equation for Elko spinor fields, which resembles but is different from the Dirac equation.

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Notes

  1. Our use of the indices + −and − +differs slightly from the one of [12] since our first index refers to left component and the second one to right component, which is opposed to [12]. However, this is the natural choice for us because of the relation between left and right components as in (32).

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Acknowledgements

We are grateful to Dr. R. da Rocha for reading the manuscript, discussions and suggestions.

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  1. Departamento de Matemática Aplicada - IMECC, Universidade Estadual de Campinas (UNICAMP), 13081-970, Campinas, SP, Brazil

    Jayme Vaz Jr.

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  1. Jayme Vaz Jr.
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Vaz, J. The Clifford Algebra of Physical Space and Elko Spinors. Int J Theor Phys 57, 582–601 (2018). https://doi.org/10.1007/s10773-017-3591-4

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