Supersymmetry and the Dirac oscillator

Journal Article · Wed Apr 10 04:00:00 EDT 1991 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X91000836· OSTI ID:5006240

Quesne, C ^[1]

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1. Physique Nucleaire Theorique et Physique Mathematique CP229, Universite Libre de Bruxelles, Bd du Triumphe, B1050 Bruxelles (BE)

This paper demonstrates the realization of supersymmetric quantum mechanics in the first-order Dirac oscillator equation by associating with it another Dirac equation, which may be considered as its supersymmetric partner. The authors show that both the particle and the antiparticle spectra, resulting from these two equations after filling the negative-energy states and redefining the physical ground state, indeed present the degeneracy pattern characteristic of unbroken supersymmetry. In addition, the authors analyze in detail two algebraic structures, each partially explaining the degeneracies present in the Dirac oscillator supersymmetric spectrum in the non-relativistic limit. One of them is the spectrum-generating superalgebra osp(2/2, R), first proposed by Balantekin. The authors prove that it is closely connected with the supersymmetric structure of the first-order Dirac oscillator equation as its odd generators are the two sets of supercharges respectively associated with the equation and its supersymmetric partner. The other algebraic structure is an so (4) {circle plus} so (3, 1) algebra, which is an extension of a similar algebra first considered by Moshinsky and Quesne. The authors prove that it is the symmetry algebra of the Dirac oscillator supersymmetric Hamiltonian. Some possible relations between the spectrum-generating superalgebra, the symmetry algebra, and their respective subalgebras are also suggested.

• OSTI ID: 5006240
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 6:9; ISSN 0217-751X; ISSN IMPAE
• Country of Publication: United States
• Language: English

Related Subjects

645300* -- High Energy Physics-- Particle Invariance Principles & Symmetries
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTIMATTER
ANTIPARTICLES
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELEMENTARY PARTICLES
ENERGY LEVELS
EQUATIONS
GROUND STATES
HAMILTONIANS
MATHEMATICAL OPERATORS
MATTER
MECHANICS
NEGATIVE ENERGY STATES
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
QUANTUM MECHANICS
QUANTUM OPERATORS
SUPERSYMMETRY
SYMMETRY
SYMMETRY BREAKING
WAVE EQUATIONS