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From a world-sheet supersymmetry to the Dirac equation

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Il Nuovo Cimento A (1965-1970)

Summary

Starting from a classical action for a point particle with a local world-sheet supersymmetry, the Dirac equation follows with operators\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\alpha } ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } \) and\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\gamma } \) being defined in the Grassmann space as differential operators and having all the properties of the corresponding Dirac matrices except that\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\alpha } \) and\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } \) are anti-Hermitian rather than Hermitian. Such a particle interacts with an external field as expected.

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Authors and Affiliations

  1. Department of Physics, University of Ljubljana, Jadranska 19, 61111, Ljubljana, Yugoslavia

    N. Mankoč-Borštnik

  2. J. Stefan Institute, University of Ljubljana, Jamova 39, 61111, Ljubljana

    N. Mankoč-Borštnik

Authors
  1. N. Mankoč-Borštnik
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Additional information

The work was supported by the Research Fund of Slovenia and the National Science Fundation through funds made available to the US — Yugoslav Joint Board for Scientific and Technological Cooperation (Contract No. NSF 899).

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Mankoč-Borštnik, N. From a world-sheet supersymmetry to the Dirac equation. Nuov Cim A 105, 1461–1471 (1992). https://doi.org/10.1007/BF02731978

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  • DOI: https://doi.org/10.1007/BF02731978

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