Il Nuovo Cimento A (1965-1970)

, Volume 35, Issue 3, pp 377–399 | Cite as

Supersymmetries and the pseudoclassical relativistic electron

  • A. Barducci
  • R. Casalbuoni
  • L. Lusanna


In this work we consider a version of the supersymmetry parametrized by anticommuting pseudovector and pseudoscalar variables instead of spinorial ones. We construct a pseudoclassical relativistic Lagrangian invariant under the former supersymmetry. This Lagrangian is a degenerate one and we show that, after quantization, one of the constraints gives rise to the Dirac equation. Moreover, we introduce into our Lagrangian an interaction term with an external electromagnetic field, and we show that this is possible, in a consistent way, only if the anomalous magnetic moment is vanishing. It follows that this model represents a pseudoclassical description for the relativistic electron.

Суперсимметрии и псевдоклассический релятивистский злектрон


В зтой работе мы рассматриваем вариант суперсимметрии, пара-метриэованной с помошью антикоммутирующих псевдовекторБых и псевдоскаляр-ных переменных, вместо спинорных переменных. Мы конструируем псевдокласси-ческий релятивистский Лагранжиан, инвариантный относительно первой иэ выщеу-каэанных суперсимметрий. Этот Лагранжиан является вырожденным и мы по-каэываем, что после квантования одно иэ ограничений приводит к уравнению Ди-рака. Кроме того, мы вводим в нащ Лагранжиан член вэаимодействия с внещним злектромагнитным полем. Мы покаэываем, что зто воэможно сделать непротиво-речивым обраэом, если только аномальный магнитный момент обрашается в нуль. Иэ зтого следует, что предложенная модель представляет псевдоскалярное описание для релятивистского злектрона.


In questo lavoro si considera una versione della supersimmetria la cui parametrizzazione è effettuata in termini di variabili anticommutanti pseudovettoriali e pseudoscalari invece che spinoriali. Si costruisce una Lagrangiana relativistica pseudoclassica invariante rispetto alla precedente supersimmetria. Questa Lagrangiana risulta degenere e si mostra che, dopo quantizzazione, uno dei vincoli dà luogo alla equazione di Dirac. Nella nostra Lagrangiana si introduce inoltre un termine di interazione con un campo elettromagnetico esterno, e si mostra che ciò è possibile in maniera consistente solo se il momento magnetico anomalo è nullo. Segue che questo modello rappresenta una descrizione pseudoclassica per l’elettrone relativistico.


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Copyright information

© Società Italiana di Fisica 1976

Authors and Affiliations

  • A. Barducci
    • 1
    • 2
  • R. Casalbuoni
    • 2
  • L. Lusanna
    • 2
  1. 1.Istituto di Fisica Teorica dell’UniversitàFirenze
  2. 2.Istituto Nazionale di Fisica NucleareSezione di FirenzeItaly

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