Semiclassical Description of Relativistic Spin without use of Grassmann variables and the Dirac equation

Understand

We propose a relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation.

• Both $\Gamma$\,-matrices and the relativistic spin tensor are produced through the canonical quantization of the classical variables which parametrize the properly constructed relativistic spin surface.
• Although there is no mass-shell constraint in our model, our particle's speed cannot exceed the speed of light.
• The classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory.