Dirac oscillator and nonrelativistic Snyder-de Sitter algebra

doi:10.1063/1.4905085

Title: Dirac oscillator and nonrelativistic Snyder-de Sitter algebra

Full Record
Other Related Research

Abstract

Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.

Authors:

Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua ^[1]

Department of Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov Str., Lviv, UA-79005 (Ukraine)

Publication Date:: Thu Jan 15 00:00:00 EST 2015

OSTI Identifier:: 22403079

Resource Type:: Journal Article

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COMMUTATION RELATIONS; DE SITTER GROUP; DE SITTER SPACE; ENERGY SPECTRA; OSCILLATORS; QUANTUM MECHANICS; SUPERSYMMETRY

Citation Formats


                    Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua. Dirac oscillator and nonrelativistic Snyder-de Sitter algebra.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4905085.

Copy to clipboard


                    Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua. Dirac oscillator and nonrelativistic Snyder-de Sitter algebra.  United States.  https://doi.org/10.1063/1.4905085

Copy to clipboard


                    Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua. 2015.  
        "Dirac oscillator and nonrelativistic Snyder-de Sitter algebra".  United States.  https://doi.org/10.1063/1.4905085.

Copy to clipboard


                    
@article{osti_22403079,

  title        = {Dirac oscillator and nonrelativistic Snyder-de Sitter algebra},

  author       = {Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua},

  abstractNote = {Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.},

  doi          = {10.1063/1.4905085},

  url          = {https://www.osti.gov/biblio/22403079},
  journal      = {Journal of Mathematical Physics},

  issn         = {0022-2488},

  number       = 1,

  volume       = 56,

  place        = {United States},

  year         = {Thu Jan 15 00:00:00 EST 2015},

  month        = {Thu Jan 15 00:00:00 EST 2015}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1063/1.4905085

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Higher spin de Sitter Hilbert space

Journal Article Anninos, Dionysios; Denef, Frederik; Monten, Ruben; ... - Journal of High Energy Physics (Online)

We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The fundamental degrees of freedom are 2N bosonic fields living on the future conformal boundary, where N is proportional to the de Sitter horizon entropy. The vacuum state is normalizable. The model agrees in perturbation theory with expectations from a previously proposed dS-CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves the apparent pathologies affecting the Sp(N) model,more »« less
https://doi.org/10.1007/jhep10(2019)071

Full Text Available
Discrete symmetries and de Sitter spacetime

Journal Article Pascu, Gabriel - AIP Conference Proceedings

Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
https://doi.org/10.1063/1.4903010
Kappa Snyder deformations of Minkowski spacetime, realizations, and Hopf algebra

Journal Article Meljanac, S; Meljanac, D; Samsarov, A; ... - Physical Review. D, Particles Fields

We present Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra. These deformations interpolate between Snyder and {kappa}-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. By introducing modules, it is shown that, although deformed and undeformed structures are not isomorphic at the level of vector spaces, they are isomorphic at the level of Hopf-algebraic action on corresponding modules. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from {kappa}-deformed Snyder to Snyder space is constructed. The deformed Leibniz rule, the Hopf structure, and the star product are found. Specialmore »« less
https://doi.org/10.1103/PHYSREVD.83.065009
Self-adjointness-based quantum field theory in de Sitter and anti--de Sitter space-time

Journal Article Rumpf, H - Phys. Rev. D; (United States)

As an alternative to existing quantization schemes, the self-adjointness of the classical field equations is employed as the basic principle for the quantization of a scalar field of arbitrary mass m. The results thus obtained in de Sitter space differ markedly from previous ones based on the so-called Euclidean approach to quantum field theory. It is argued that if m/sup 2/>(4R/sup 2/)/sup -1/ (R is the de Sitter radius) a geodesic observer will detect a constant flux of particles coming from the cosmological event horizon. In contrast to the result of Gibbons and Hawking, however, the spectrum is nonthermal. Formore »« less
https://doi.org/10.1103/PhysRevD.24.275
Supersymmetry and the Dirac oscillator

Journal Article Quesne, C - International Journal of Modern Physics A; (United States)

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,more »« less
https://doi.org/10.1142/S0217751X91000836

Similar Records