najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2022-13-3-299-307najo-241Research ArticleСтатьиLadder operators approach to representation classi cation problem for Jordan-Schwinger image of su(2) algebraTushavinG. V.gleb@tushavin.ruZaitsevaE. V.zaytceva.workmail@gmail.comTrifanovA. I.alextrifanov@gmail.comITMO UniversityRussian Federation202206062025133299307Copyright © Tushavin G.V., Zaitseva E.V., Trifanov A.I., 20252025Tushavin G.V., Zaitseva E.V., Trifanov A.I.Tushavin G.V., Zaitseva E.V., Trifanov A.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/241

The eigenvalues of the complete commuting set of self-adjoint operators determine the classi cation of states. We construct a classi cation for the image of the Jordan-Schwinger mapping of the su (2) algebra. We use the ladder operator approach to construct a canonical basis of irreducible representations and de ne the self-adjoint operators of the complete commuting set.

Ladder operatorssu(2)Jordan-Schwinger maprepresentation theoryReferencesWilliams C.L., Pandya N.N., Bodmann B.G., Kouri D.J. Coupled supersymmetry and ladder structures beyond the harmonic oscillator. Molecular Physics, 2018, 116 (19-20), P. 2599-2612.Williams C.L., Pandya N.N., Bodmann B.G., Kouri D.J. Coupled supersymmetry and ladder structures beyond the harmonic oscillator. Molecular Physics, 2018, 116 (19-20), P. 2599-2612.Hoffmann S.E., Hussin V., Marquette I., Zhang Y.-Z. Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator. J. Math. Phys., 2019, 60, 052105.Hoffmann S.E., Hussin V., Marquette I., Zhang Y.-Z. Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator. J. Math. Phys., 2019, 60, 052105.Bosso P., Das S. Generalized ladder operators for the perturbed harmonic oscillator. Ann. of Phys., 2018, 396, P. 254-265.Bosso P., Das S. Generalized ladder operators for the perturbed harmonic oscillator. Ann. of Phys., 2018, 396, P. 254-265.Aouda K., Kanda N., Naka S., Toyoda H. Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect. Phys. Rev. D, 2020, 102, 025002.Aouda K., Kanda N., Naka S., Toyoda H. Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect. Phys. Rev. D, 2020, 102, 025002.Weyl H., Robertson H.P. The theory of groups and quantum mechanics, Dover Publications, New York, 1950.Weyl H., Robertson H.P. The theory of groups and quantum mechanics, Dover Publications, New York, 1950.Perelomov A.M. Generalized Coherent States and Their Applications, Springer, Berlin, 1986.Perelomov A.M. Generalized Coherent States and Their Applications, Springer, Berlin, 1986.Biedenharn L.C., Louck J.D. Angular momentum in quantum physics, Cambridge univerisity press, Cambridge, 1984.Biedenharn L.C., Louck J.D. Angular momentum in quantum physics, Cambridge univerisity press, Cambridge, 1984.Miroshnichenko G.P., Kiselev A.D., Trifanov A.I., Gleim A.V. Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model. J. Opt. Soc.Am. B, 2017, 34 (6), P. 1177-1190.Miroshnichenko G.P., Kiselev A.D., Trifanov A.I., Gleim A.V. Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model. J. Opt. Soc.Am. B, 2017, 34 (6), P. 1177-1190.Gelfand I.D., Shapiro Z.Ya., Minlos R.A. Representations of the Rotation and Lorentz Groups and Their Applications, The Pergamon Press, Oxford, 1963.Gelfand I.D., Shapiro Z.Ya., Minlos R.A. Representations of the Rotation and Lorentz Groups and Their Applications, The Pergamon Press, Oxford, 1963.Tushavin G.V., Trifanov A.I., Trifanova E.S., Shipitsyn I.A. Structure of invariant subspaces of the rotation group image under the Jordan mapping. 2019 Days on Diffraction (DD), 2019, St. Petersburg, Russia, P. 216-220.Tushavin G.V., Trifanov A.I., Trifanova E.S., Shipitsyn I.A. Structure of invariant subspaces of the rotation group image under the Jordan mapping. 2019 Days on Diffraction (DD), 2019, St. Petersburg, Russia, P. 216-220.

The authors declare that there are no conflicts of interest present.