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

Abstract

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. In particular, the position variable experiences {\it Zitterbewegung} in noninteracting theory. The classical equations for the spin tensor are the same as those of the Barut-Zanghi model of a spinning particle.

16 pages, misprints corrected

References in corpus (3)

• Conversion of second class constraints by deformation of Lagrangian local symmetries
• Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung
• On the dynamics of classical particle with spin

Cited by in corpus (10)

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• Lagrangian for Frenkel electron and position's non-commutativity due to spin
• Frenkel electron and a spinning body in a curved background
• Rigid particle revisited: extrinsic curvature yields the Dirac equation
• Very Special Relativity and Lorentz Violating Theories
• Geometric Constructions Underlying Relativistic Description of Spin on the Base of Non-Grassmann Vector-Like Variable
• Variational problem for the Frenkel and the Bargmann-Michel-Telegdi (BMT) equations
• Classical-mechanical models without observable trajectories and the Dirac electron
• Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin
• Non-Grassmann mechanical model of the Dirac equation