Research on elementary particle physics: Task P, Studies in theory and phenomenology of elementary particles Page: 4 of 7
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Progress in Theory
The major progress in theory this year has been the discovery by L.M. Jones of
a new Dirac equation for the harmonic oscillator. This involves a)finding an (appar-
ently previously unknown) linear equation for the "or inary" harmonic oscillator,
b)extending this to space-time, c)"mating" it with the Dirac gamma matrices to
form a Dirac-type equation, and d)finding some classes of solutions. The work is
described in a preprint, "Another Dirac Oscillator", which has been submitted for
The Dirac oscillator is of interest to persons attempting wave-function mod-
elling of confined systems (after all, we really can only solve the harmonic oscillator
and the hydrogen atom in any great detail, without resorting to numerical meth-
ods); it is convenient to have a "toy model" with analytic solutions to play with.
Our interest in the model arose because of a continuing desire to examine sys-
tems in which anti-commuting (Grassmannian) coordinates are adjoined to space-
time. Efforts are continuing to understand the algebraic structure of the Lorentz
group extension to these coordinates . In working with these algebraic relations,
it appeared that we would need operators in the ordinary space-time sector which
had similar form to those in the Grassmannian sector. The linear operators used
in our harmonic oscillator analysis are of this general form.
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Research on elementary particle physics: Task P, Studies in theory and phenomenology of elementary particles, report, May 1, 1992; United States. (https://digital.library.unt.edu/ark:/67531/metadc1057609/m1/4/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.