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The Dirac Equation as One Fourth-Order Equation for One Function: A General, Manifestly Covariant Form

  • Andrey Akhmeteli
Chapter
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)

Abstract

Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac spinor function. This was done for a specific (chiral) representation of gamma matrices and for a specific component. In the current work, the result is generalized for a general representation of gamma matrices and a general component (satisfying some conditions). The resulting equivalent of the Dirac equation is also manifestly relativistically covariant and should be useful in applications of the Dirac equation.

Notes

Acknowledgements

The author is grateful to V.G. Bagrov, A.V. Gavrilin, A.Yu. Kamenshchik, P.W. Morgan, nightlight, R. Sverdlov, and H. Westman for their interest in this work and valuable remarks.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Andrey Akhmeteli
    • 1
  1. 1.LTASolid Inc.HoustonUSA

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