Jordan, T. F. ; Mukunda, N.
(1963)
*Lorentz-covariant position operators for spinning particles*
Physical Review, 132
(4).
pp. 1842-1848.
ISSN 0031-899X

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Official URL: http://prola.aps.org/abstract/PR/v132/i4/p1842_1

Related URL: http://dx.doi.org/10.1103/PhysRev.132.1842

## Abstract

An examination is made of the consequences for the quantum mechanics of spinning particles of equations characteristic of Lorentz-covariant position variables. These equations are commutator analogs of the Poisson bracket equations that express the familiar transformation properties of space-time events in classical mechanics. For a particle of zero spin it is found that the usual canonical coordinate is the unique solution of these equations. For a particle with positive spin there is no position operator which satisfies these equations and has commuting components. For a particle and antiparticle there is a unique solution with commuting components which is valid for all values of the spin and reduces for zero spin to the canonical coordinate. For spin 1/2 this is the Foldy-Wouthuysen transform of the position operator of the Dirac equation. A generalization of the inverse Foldy-Wouthuysen transformation, valid for any value of the spin, appears as a unique unitary transformation which takes this generalized Dirac position to the canonical coordinate. The application of this transformation to the canonical form of the Hamiltonian gives a generalization of the Dirac equation Hamiltonian. This is developed and compared with the literature for spin 1. It gives a nonlocal equation as the spin 1 analog of the Dirac equation.

Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |

ID Code: | 25324 |

Deposited On: | 06 Dec 2010 13:35 |

Last Modified: | 08 Jun 2011 05:38 |

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