Zitterbewegung and the internal geometry of the electron

Journal Article · Fri May 15 04:00:00 EDT 1981 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.23.2454· OSTI ID:6498506

Barut, A O; Bracken, A J

Schroedinger's work on the Zitterbewegung of the free electron is reexamined. His proposed ''microscopic momentum'' vector for the Zitterbewegung is rejected in favor of a ''relative momentum'' vector, with the value P = mca in the rest frame of the center of mass. His oscillatory ''microscopic coordinate'' vector is retained. In the rest frame, it takes the form Q = -i(h/2mc)ba, and the Zitterbewegung is described in this frame in terms of P, Q, and the Hamiltonian mc/sup 2/b, as a finite three-dimensional harmonic oscillator with a compact phase space. The Lie algebra generated by Q and P is that of SO(5), and in particular (Q/sub i/,P/sub j/) = -ihd/sub i/jb. It is argued that the simplest possible finite, three-dimensional, isotropic, quantum-mechanical system requires such an SO(5) structure, incorporates a fundamental length, and has harmonic-oscillator dynamics. Dirac's equation is derived as the wave equation appropriate to the description of such a finite quantum system in an arbitrary moving frame of reference, using a dynamical group SO(3,2) which can be extended to SO(4,2). Spin appears here as the orbital angular momentum associated with the internal system, and rest-mass energy appears as the internal energy in the rest frame. Possible generalizations of these ideas are indicated, in particular those involving higher-dimensional representations of SO(5).

• Research Organization: Department of Physics, University of Colorado, Boulder, Colorado 80309
• OSTI ID: 6498506
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 23:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRONIC EQUIPMENT
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
EQUIPMENT
FERMIONS
HAMILTONIANS
HARMONIC OSCILLATORS
HEISENBERG PICTURE
LEPTONS
LIE GROUPS
LORENTZ TRANSFORMATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
PHASE SPACE
QUANTUM OPERATORS
RENORMALIZATION
SO GROUPS
SPACE
SPACE-TIME
SPIN
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS
ZITTERBEWEGUNG