Supersymmetric properties and stability of the Dirac sea

Journal Article · Fri Mar 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.2036· OSTI ID:5845992

Martriaanez y Romero, R P ^[1]; Moreno, M ^[2]; Zentella, A ^[3]

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1. Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-542, 04510 Mexico, Distrito Federal (Mexico)
2. Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico, Distrito Federal (Mexico) Fermi National Laboratory, P.O. Box 500, Batavia, Illinois 60510 (USA)
3. Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico, Distrito Federal (Mexico)

In this work we construct a superalgebra for potential problems in the Dirac equation. We show that this superalgebra is closed for the large class of interactions that leave the Dirac sea stable. In this case, we find that it is possible to perform an exact SU(2) transformation for the Dirac Hamiltonian of the problem. This procedure is formally equivalent to obtaining an exact form for the related Foldy-Wouthuysen Hamiltonian. The potential problems that can be exactly diagonalized include the Dirac oscillator, an arbitrary, time-independent magnetic field, and all the odd potentials, as well as its non-Abelian generalizations. We find that the internal group generators do not destroy the structure of the superalgebra. We work out explicitly the example of the Dirac oscillator.

• OSTI ID: 5845992
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:6; ISSN PRVDA; ISSN 0556-2821
• 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
CANONICAL TRANSFORMATIONS
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FIELD THEORIES
FOLDY-WOUTHUYSEN TRANSFORM
FUNCTIONS
HAMILTONIANS
HARMONIC OSCILLATOR MODELS
KLEIN-GORDON EQUATION
LIE GROUPS
MAGNETIC FIELDS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SU GROUPS
SU-2 GROUPS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS
WAVE FUNCTIONS