Rigid particle revisited: Extrinsic curvature yields the Dirac equation

@article{Deriglazov2013RigidPR,
  title={Rigid particle revisited: Extrinsic curvature yields the Dirac equation},
  author={Alexei A. Deriglazov and Armen Nersessian},
  journal={Physics Letters A},
  year={2013},
  volume={378},
  pages={1224-1227}
}
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18 Citations
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18 Citations

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References

SHOWING 1-10 OF 38 REFERENCES

Canonical Quantization of a Rigid Particle

We quantize a rigid particle with a rigidity term proportional to the square of the extrinsic curvature of the particle's world-line using the Dirac-Bergmann scheme. Problems concerning higher order…

The Quantization of a Point Particle With Extrinsic Curvature Leads to the Dirac Equation

Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung

Hamiltonian formalism for particles with a generalized rigidity

The Hamiltonian formalism is developed for mechanical systems described by reparametrization-invariant Lagrangians dependent on the external curvatures of a world line. The complete sets of…

Classical-mechanical models without observable trajectories and the Dirac electron

A semiclassical description of relativistic spin without the use of Grassmann variables and the Dirac equation

The Hamiltonian Formalism in the Model of the Relativistic String With Rigidity

The model of the bosonic string with the Nambu-Goto action extended by the term proportional to the external curvature of the world sheet is explored. The external curvature of the world sheet is…

Singular Lagrangians with higher derivatives

The Hamiltonian formalism for systems with singular Lagrangians of the second order is constructed. A new method is proposed for obtaining the equations of motion in the phase space for theories with…

Relativistic particle with curvature in an external electromagnetic field

A model of a relativistic particle with curvature interacting with an external electromagnetic field in a “minimal way” is investigated. The generalized Hamiltonian formalism for this model is…

A GEOMETRICAL PARTICLE MODEL FOR ANYONS

We consider the simplest geometrical particle model associated with light-like curves in (2+1) dimensions. The action is proportional to the pseudo-arc length of the particle's path. We show that…