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 |
Darbyshire Operator, Dirac Matrices, Gamma Matrices, Matrix Theory, Quantum Mechanics
| [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. |
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
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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Download@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}
}
TY - JOUR T1 - Extending the 4 × 4 Darbyshire Operator Using n-Dimensional Dirac Matrices AU - Paul M. Darbyshire Y1 - 2016/02/19 PY - 2016 N1 - https://doi.org/10.11648/j.ijamtp.20150103.11 DO - 10.11648/j.ijamtp.20150103.11 T2 - International Journal of Applied Mathematics and Theoretical Physics JF - International Journal of Applied Mathematics and Theoretical Physics JO - International Journal of Applied Mathematics and Theoretical Physics SP - 19 EP - 23 PB - Science Publishing Group SN - 2575-5927 UR - https://doi.org/10.11648/j.ijamtp.20150103.11 AB - 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. VL - 1 IS - 3 ER -
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