The Dirac oscillator and local automorphism invariance

James P. Crawford

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form (ar2+bL·S), where a and b are constants. To obtain the Dirac oscillator, a "minimal substitution" is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, a very unusual feature of the covariant derivative in this case is that the potential is a nontrivial element of the Clifford algebra. A theory which naturally gives rise to gauge potentials which are nontrivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the pure automorphism gauge field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented herein.

Original languageEnglish (US)
Pages (from-to)4428-4435
Number of pages8
JournalJournal of Mathematical Physics
Volume34
Issue number10
DOIs
StatePublished - Jan 1 1993

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Automorphism
Paul Adrien Maurice Dirac
invariance
Invariance
oscillators
Covariant Derivative
Clifford Algebra
algebra
Klein-Gordon equation
Klein-Gordon Equation
Dirac Equation
Gauge Field
Term
Dirac equation
Harmonic Oscillator
harmonic oscillators
Substitution
Gauge
Exact Solution
substitutes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Crawford, James P. / The Dirac oscillator and local automorphism invariance. In: Journal of Mathematical Physics. 1993 ; Vol. 34, No. 10. pp. 4428-4435.
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The Dirac oscillator and local automorphism invariance. / Crawford, James P.

In: Journal of Mathematical Physics, Vol. 34, No. 10, 01.01.1993, p. 4428-4435.

Research output: Contribution to journalArticle

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