Supersymmetries and the pseudoclassical relativistic electron

• DOI: 10.1007/bf02730291
• Publication Date: 2007-12-18T08:40:00Z
• Authors: A. Barducci; R. Casalbuoni; L. Lusanna
• Keywords: 0103 physical sciences; 01 natural sciences

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.