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Separation of Angular Momentum

Received: 7 December 2015    Accepted: 26 January 2016    Published: 16 February 2016
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Abstract

In this paper we speak about angular momentum, we have shown that the separation of the total angular momentum of the electromagnetic field into its orbital and spin parts. It is dictated by quantum mechanics of photons reproduces. Therefore, the results are derived from the proprieties of Fourier and Maxwell fields by Darwin, with the correspondence results that derived heuristically by many authors.

Published in American Journal of Applied Mathematics (Volume 4, Issue 1)
DOI 10.11648/j.ajam.20160401.14
Page(s) 47-52
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Angular Momentum of Light, Quantum Mechanics of Photons, Riemann-Silberstien Vector

References
[1] Iwo Bialynicki-Birula and Zofia Bialynicki-Birula 2011 Canonical separation of angular momentum of light into its orbital and spin parts.
[2] Lomont J S and Moses H E 1962 Simple realizations of the infinitesimal generators of the proper orthochronous inhomogeneous Lorentz group for mass zero J. Math. Phys.
[3] Bialynicki-Birula I and Bialynicka-Birula Z 1975 Quantum Electrodynamics (Oxford: Pergamon).
[4] Bialynicki-Birula I and Bialynicka-Birula Z 1987 Berry’s phase in the relativistic theory of spinning particles Phys. Rev. D 35 2383.
[5] Bialynicki-Birula I 1996 Photon wavefunction Progress in Optics vol 36, ed E Wolf (Amsterdam: Elsevier).
[6] Bialynicki-Birula I and Bialynicka-Birula Z 2006 Beams of electromagnetic radiation carrying angular momentum: the Riemann–Silberstein vector and the classical-quantum correspondence Opt. Commune.
[7] Rob Van der Vorst. Introduction to differential manifolds.
[8] John M. Lee.. Introduction to smooth manifolds.
[9] M. E. Rose, Relativistic electron theory (John Wiley & Sons, New York, 1961).
[10] O. Hosten and P. Kwiat, Science 319, 787 (2008).
[11] Barnett S M 2010 Rotation of electromagnetic fields and thenature of optical angular momentum J. Mod.
[12] Li C-F 2009 Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization.
[13] Allen L, Barnett S M and Padget M J 2003 Optical Angular Momentum (Bristol: Institute of Physics Publishing) This is a collection of papers with introductory material by the editors.
[14] Lenstra D and Mandel L 1982 Angular momentum of the quantized electromagnetic field with periodic boundary conditions Phys. Rev. 26 3428.
[15] J`aregui R and Hacyan S 2005 Quantum-mechanical properties of Bessel beams Phys. Rev. A 71 033411.
[16] Calvo G F, Pic`on A and Bagan E 2006 Quantum field theory of photons with orbital angular momentum Phys. Rev. A 73 013805.
[17] Aiello A, Marquardt C and Leuchs G 2009 Transverse angular momentum of photons Phys. Rev. A 81 053838.
[18] Cohen-Tannoudji C, Dupont-Roc J and Grynberg G 1989 Photons and Atoms: Introduction to Quantum Electrodynamics (New York: Wiley) chapter 1.
[19] Schweber S S 1961 An Introduction to Relativistic Quantum Field Theory (Evanston: Row, Peterson and Co) chapter 9.
[20] D. F. Walls, Nature, 301(1983)141; R. W. Henry and S. C. Glotzer, Am. J. Phys. 56, 4, (1988) 318; M. M. Nieto, in Frontiers of Non-equilibrium Statistical Mechanics, Proceedings of NATO Advanced Study Institute, ed. G. T. Moore and M. O. Scully, Plenum, NY.
[21] B. Yurke, S. L. McCall, J. R. Klauder, Phys. Rev. A33 6 (1986) 4033; M. Hillery and L. Mlodinow, Phys. Rev. A48, 2 (1993) 1548.
[22] E. P. Wigner in Group Theory and its applications to the Quantum Mechanics of Atomic Spectra, Academic Press, NY (1959); A. Vaglica and G. Vetri, Optics Communications, 51, 4 (1984) 239.
[23] J. Schwinger in Quantum theory of Angular Momentum, ed. L. Beidenharn and H. van Dam, Academic Press, NY. (1965) 22.
[24] Most general result can be found in the doctoral Thesis of Abir Bandyopadhyay, submitted on December 13, 1996, and successfully defended on November 27, 1997, at Indian Institute of Tecnology, Kanpur. Also corrected electronic copy is available on request from him through email.
[25] G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, Phys. Rev. Lett. 94, 170403 (2005).
[26] S. M. Barnett, Phys. Rev. Lett. 104, 070401 (2010).
[27] T. Ramos, G. F. Rubilar, and Y. N. Obukhov, Phys. Lett. A 375, 1703 (2011).
[28] F. W. Hehl and Y. N. Obukhov, Foundations of Classical Electrodynamics: Charge, Flux, and Metric (Birkh¨auser, Boston, 2003).
[29] Cf. Bendixson (1901, p. 11 and next); Coddington and Levinson (1955, p. 391 and next); Hirsch et al. (2004, p. 225 and next).
[30] Cf. Guckenheimer and Holmes (1983, p. 141); Wiggins (1990, p. 212); Dang-Vu (2000, p. 47).
Cite This Article
  • APA Style

    Mohammed Yousif, Emadaldeen Abdalrahim. (2016). Separation of Angular Momentum. American Journal of Applied Mathematics, 4(1), 47-52. https://doi.org/10.11648/j.ajam.20160401.14

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    ACS Style

    Mohammed Yousif; Emadaldeen Abdalrahim. Separation of Angular Momentum. Am. J. Appl. Math. 2016, 4(1), 47-52. doi: 10.11648/j.ajam.20160401.14

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    AMA Style

    Mohammed Yousif, Emadaldeen Abdalrahim. Separation of Angular Momentum. Am J Appl Math. 2016;4(1):47-52. doi: 10.11648/j.ajam.20160401.14

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  • @article{10.11648/j.ajam.20160401.14,
      author = {Mohammed Yousif and Emadaldeen Abdalrahim},
      title = {Separation of Angular Momentum},
      journal = {American Journal of Applied Mathematics},
      volume = {4},
      number = {1},
      pages = {47-52},
      doi = {10.11648/j.ajam.20160401.14},
      url = {https://doi.org/10.11648/j.ajam.20160401.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160401.14},
      abstract = {In this paper we speak about angular momentum, we have shown that the separation of the total angular momentum of the electromagnetic field into its orbital and spin parts. It is dictated by quantum mechanics of photons reproduces. Therefore, the results are derived from the proprieties of Fourier and Maxwell fields by Darwin, with the correspondence results that derived heuristically by many authors.},
     year = {2016}
    }
    

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    JO  - American Journal of Applied Mathematics
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    AB  - In this paper we speak about angular momentum, we have shown that the separation of the total angular momentum of the electromagnetic field into its orbital and spin parts. It is dictated by quantum mechanics of photons reproduces. Therefore, the results are derived from the proprieties of Fourier and Maxwell fields by Darwin, with the correspondence results that derived heuristically by many authors.
    VL  - 4
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Author Information
  • Sudan University of Science and Technology (SUST), College of Science, Khartoum, Sudan

  • Sudan University of Science and Technology (SUST), College of Science, Khartoum, Sudan

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