Classical-mechanical models without observable trajectories and the Dirac electron

Abstract

We construct a non-Grassmann spinning-particle model which, by analogy with quantum mechanics, does not admit the notion of a trajectory within the position space. The pseudo-classical character of the model allows us to avoid the inconsistencies arising in the quantum-mechanical interpretation of a one-particle sector of the Dirac equation.

6 pages, published version

References in corpus (8)

• Quantum simulation of the Dirac equation
• Chirality Quantum Phase Transition in the Dirac oscillator
• Poincare covariant mechanics on noncommutative space
• Noncommutative relativistic particle on the electromagnetic background
• Quantum mechanics on noncommutative plane and sphere from constrained systems
• Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung
• Semiclassical Description of Relativistic Spin without use of Grassmann variables and the Dirac equation
• Reconstruction of higher stage first class constraints into the secondary ones

Cited by in corpus (9)

• Lagrangian for Frenkel electron and position's non-commutativity due to spin
• Frenkel electron on an arbitrary electromagnetic background and magnetic Zitterbewegung
• Frenkel electron and a spinning body in a curved background
• Rigid particle revisited: extrinsic curvature yields the Dirac equation
• 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
• Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin
• Remarks on generalized uncertainty principle induced from constraint system
• To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models