LORENTZ-COVARIANT POSITION OPERATORS FOR SPINNING PARTICLES

Journal Article · Fri Nov 15 04:00:00 EST 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.132.1842· OSTI ID:4156821

Jordan, T F; Mukunda, N

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 tuere 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 FoldyWouthuysen transform of tue position operator of the Dirac equation. A generalization of the inverse FoldyWouthuysen 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 cf the Dirac equation. (auth)

• Research Organization: Univ. of Rochester, N.Y.
• NSA Number: NSA-18-000891
• OSTI ID: 4156821
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 132; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANTIPARTICLES
BOSONS
COMMUTATION RELATIONS
COMMUTATORS
CONFIGURATION
DIFFERENTIAL EQUATIONS
DIRAC EQUATIONS
ELEMENTARY PARTICLES
FERMIONS
FOLDY-WOUTHUYSEN TRANSFORM
HAMILTONIAN
LORENTZ TRANSFORMATIONS
NUMERICALS
PHYSICS
QUANTUM MECHANICS
RELATIVITY THEORY
SPIN