Charge conjugation and Maiorana spinors in dimension 8

Pertti Lounesto

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 289-293
  • ISSN: 0137-6934

Abstract

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It is a common belief among theoretical physicists that the charge conjugation of the Dirac equation has an analogy in higher dimensional space-times so that in an 8-dimensional space-time there would also be Maiorana spinors as eigenspinors of a charge conjugation, which would swap the sign of the electric charge of the Dirac equation. This article shows that this mistaken belief is based on inadequate distinction between two kinds of charge conjugation: the electric conjugation swapping the sign of the Dirac equation and the Maiorana conjugation fixing the real subalgebra (of the complexification of the Clifford algebra of the space-time). Only the latter conjugation has Maiorana spinors as its eigenspinors.

How to cite

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Lounesto, Pertti. "Charge conjugation and Maiorana spinors in dimension 8." Banach Center Publications 37.1 (1996): 289-293. <http://eudml.org/doc/208605>.

@article{Lounesto1996,
abstract = {It is a common belief among theoretical physicists that the charge conjugation of the Dirac equation has an analogy in higher dimensional space-times so that in an 8-dimensional space-time there would also be Maiorana spinors as eigenspinors of a charge conjugation, which would swap the sign of the electric charge of the Dirac equation. This article shows that this mistaken belief is based on inadequate distinction between two kinds of charge conjugation: the electric conjugation swapping the sign of the Dirac equation and the Maiorana conjugation fixing the real subalgebra (of the complexification of the Clifford algebra of the space-time). Only the latter conjugation has Maiorana spinors as its eigenspinors.},
author = {Lounesto, Pertti},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {289-293},
title = {Charge conjugation and Maiorana spinors in dimension 8},
url = {http://eudml.org/doc/208605},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Lounesto, Pertti
TI - Charge conjugation and Maiorana spinors in dimension 8
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 289
EP - 293
AB - It is a common belief among theoretical physicists that the charge conjugation of the Dirac equation has an analogy in higher dimensional space-times so that in an 8-dimensional space-time there would also be Maiorana spinors as eigenspinors of a charge conjugation, which would swap the sign of the electric charge of the Dirac equation. This article shows that this mistaken belief is based on inadequate distinction between two kinds of charge conjugation: the electric conjugation swapping the sign of the Dirac equation and the Maiorana conjugation fixing the real subalgebra (of the complexification of the Clifford algebra of the space-time). Only the latter conjugation has Maiorana spinors as its eigenspinors.
LA - eng
UR - http://eudml.org/doc/208605
ER -

References

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  1. [1] M. Benn and R. W. Tucker, An Introduction to Spinors and Geometry with Applications in Physics, Adam Hilger, Bristol 1987. Zbl0798.53001
  2. [2] P. Budinich and A. Trautman, The Spinorial Chessboard, Berlin 1988. Zbl0653.15022
  3. [3] A. Crumeyrolle, Orthogonal and Symplectic Clifford Algebras, Spinor Structures, Kluwer Academic, Dordrecht 1990. 
  4. [4] R. Delanghe, F. Sommen, and V. Souček, Clifford Algebra and Spinor Valued Functions: A function theory for the Dirac operator, Kluwer Academic, Dordrecht 1992. Zbl0747.53001
  5. [5] F. R. Harvey, Spinors and Calibrations, Academic Press, San Diego 1990. Zbl0694.53002

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