Supersymmetric particles inN=2superspace: Phase-space variables and Hamiltonian dynamics

We consider a reparametrization-invariant model recently proposed based on the $N$-extended super-Poincaré group with central charges, which leads to trajectories on the $N$-extended Salam-Strathdee superspace. The case $N=2\mathrm{}$ is discussed in detail. We show that the $N=2\mathrm{}$ model is invariant under four real supergauge transformations generated by firstclass odd constraints which imply the Dirac equation. We introduce one bosonic (which fixes the reparametrization) and four real spinorial (which fix the supergauges) gauge conditions and calculate the Dirac brackets for the remaining unconstrained variables ($\overrightarrow{\mathrm{x}}, \overrightarrow{\mathrm{p}}, {\theta }^{\alpha }, {\overline{\theta }}^{\dot{\alpha }}$). The equations of motion are written in Hamiltonian form, with $H\propto \mathrm{Tr}\{Q_{\alpha i}, {\overline{Q}}_{\dot{\beta }i}\}$ and correspond to the Heisenberg equations of the (first) quantized theory.