Covariance, CPT and the Foldy-Wouthuysen transformation for the Dirac oscillator

Moreno, M.; Zentella, Arturo

doi:10.1088/0305-4470/22/17/003

Cited by 163 publications

(112 citation statements)

References 4 publications

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“…When combined with oscillator operators, the * −spin projection corresponds to states with positive and negative energies. This can be seen from the Foldy-Wouthuysen transformation of this problem [5,6]. The solutions of the stationary Schroedinger equation associated to (5) were originally obtained in [1] by writing…”

Section: The Algebraic Structure Of 12 and 3 Dimensional Dirac Oscilmentioning

confidence: 99%

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Sadurní¹,

Torres²,

Seligman³

2010

J. Phys. A: Math. Theor.

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Abstract.The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the known solution of the Dirac oscillator into matrix form; there one notices, that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two-dimensional. Choosing couplings that do not affect the block structure, these blow up the 2×2 matrices to 4×4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of example we apply this exact solution to calculate the evolution of entanglement.

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Section: The Algebraic Structure Of 12 and 3 Dimensional Dirac Oscilmentioning

confidence: 99%

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Sadurní¹,

Torres²,

Seligman³

2010

J. Phys. A: Math. Theor.

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“…The Dirac oscillator in a commutative space is defined by the following substitution suggested by Ito et al [15] see also [16,17,18,19],…”

Section: The Dirac Oscillator In a Noncommutative Spacementioning

confidence: 99%

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

Mirza

Mohadesi

2004

Commun. Theor. Phys.

151

127

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We study the Dirac and the klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.

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“…Moshinsky and Szczepaniak [2] christened it Dirac oscillator and renewed to a great extent the interest in the topic. The Dirac oscillator has been applied to quark confinement and supersymmetry [3] and hadron spectroscopy [4]. Its group symmetries have been studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Pseudospin symmetry and the relativistic harmonic oscillator

et al. 2004

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A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations ⌺ = S + V and ⌬ = V − S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case ⌺ = 0, for which pseudospin symmetry is exact. We also show that the case U = ⌬ = 0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

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Covariance, CPT and the Foldy-Wouthuysen transformation for the Dirac oscillator

Cited by 163 publications

References 4 publications

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

Pseudospin symmetry and the relativistic harmonic oscillator

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