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Extending the 4 × 4 Darbyshire Operator Using n-Dimensional Dirac Matrices

Received: 21 December 2015     Accepted: 4 January 2016     Published: 19 February 2016
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Abstract

In this paper, we extend the 4 × 4 Darbyshire operator to develop a new n-dimensional formalism using n-dimensional Dirac matrices. We then present a set of properties satisfied by the new operator and briefly discuss some areas of interest for potential applications.

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 1, Issue 3)
DOI 10.11648/j.ijamtp.20150103.11
Page(s) 19-23
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), 2016. Published by Science Publishing Group

Keywords

Darbyshire Operator, Dirac Matrices, Gamma Matrices, Matrix Theory, Quantum Mechanics

References
[1] Overbye, D. Physicists in Europe Find Tantalizing Hints of a Mysterious New Particle. New York Times. 2015.
[2] Dirac, P. A. M. The Quantum Theory of the Electron. Proceedings of the Royal Society. A117, 610-624. 1928.
[3] Darbyshire, P. M. A steady state solution to four-wave mixing utilising the SU (2, 2) group symmetry with mixed gratings in a Kerr type media. Optics Communications. 117, 283-289. 1995.
[4] Darbyshire, P. M. Doctoral Thesis, University of London. 1996.
[5] Darbyshire, P. M. The Development of a New Matrix Operator and its application to the Study of Nonlinear Coupled Wave Equations. Letters in Mathematical Physics. 54, 291-300. 2000.
[6] Pais, A. On Spinors in n Dimensions. Journal of Mathematical Physics. 3 (6), 1135-1139. 1962.
Cite This Article
  • APA Style

    Paul M. Darbyshire. (2016). Extending the 4 × 4 Darbyshire Operator Using n-Dimensional Dirac Matrices. International Journal of Applied Mathematics and Theoretical Physics, 1(3), 19-23. https://doi.org/10.11648/j.ijamtp.20150103.11

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    ACS Style

    Paul M. Darbyshire. Extending the 4 × 4 Darbyshire Operator Using n-Dimensional Dirac Matrices. Int. J. Appl. Math. Theor. Phys. 2016, 1(3), 19-23. doi: 10.11648/j.ijamtp.20150103.11

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    AMA Style

    Paul M. Darbyshire. Extending the 4 × 4 Darbyshire Operator Using n-Dimensional Dirac Matrices. Int J Appl Math Theor Phys. 2016;1(3):19-23. doi: 10.11648/j.ijamtp.20150103.11

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  • @article{10.11648/j.ijamtp.20150103.11,
      author = {Paul M. Darbyshire},
      title = {Extending the 4 × 4 Darbyshire Operator Using n-Dimensional Dirac Matrices},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {1},
      number = {3},
      pages = {19-23},
      doi = {10.11648/j.ijamtp.20150103.11},
      url = {https://doi.org/10.11648/j.ijamtp.20150103.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20150103.11},
      abstract = {In this paper, we extend the 4 × 4 Darbyshire operator to develop a new n-dimensional formalism using n-dimensional Dirac matrices. We then present a set of properties satisfied by the new operator and briefly discuss some areas of interest for potential applications.},
     year = {2016}
    }
    

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Author Information
  • Computational Biophysics Group, Algenet Cancer Research, Nottingham, UK

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