Lorentz-covariant position operators for spinning particles

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


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
Source:Copyright of this article belongs to American Physical Society.
ID Code:25324
Deposited On:06 Dec 2010 13:35
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