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2007 | 5 | 4 | 487-506
Tytuł artykułu

Matrix realization of dual quaternionic electromagnetism

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a new representational model based on dual quaternionic matrices is proposed for classical electromagnetism. After demonstrating the isomorphic matrix representations of dual quaternions, Maxwell’s equations and the constitutive relations for electromagnetism are expressed in terms of dual quaternionic matrices. For this purpose, new 8 × 8 matrices connected with quaternion basis elements have been introduced.
Wydawca

Czasopismo
Rocznik
Tom
5
Numer
4
Strony
487-506
Opis fizyczny
Daty
wydano
2007-12-01
online
2007-12-01
Twórcy
Bibliografia
  • [1] W.R. Hamilton: Elements of Quaternions, Chelsea Publishing, New York, 1969.
  • [2] J.C. Maxwell: A Treatise on Electricity and Magnetism, Clarendon Press, Oxford, 1873.
  • [3] I. Abonyi, J.F. Bito and J.K. Tar: “A quaternion representation of the lorentz group for classical physical applications”, J. Phys. A-Math. Gen., Vol. 24, (1991), pp. 3245–3254. http://dx.doi.org/10.1088/0305-4470/24/14/013[Crossref]
  • [4] K. Imaeda: “A new formulation of classical electrodynamics”, Nuovo Cimento B, Vol. 32, (1976), pp. 138–162. [Crossref]
  • [5] F. Colombo, P. Loustaunau, I. Sabadini and D.C. Struppa: “Regular functions of biquaternionic variables and Maxwell’s equations”, J. Geom. Phys., Vol. 26, (1998), pp. 183–201. http://dx.doi.org/10.1016/S0393-0440(97)00035-1[Crossref]
  • [6] J. Lambek: “If Hamilton had prevailed: quaternions in physics”, The Mathematical Intelligencer, Vol. 17, (1995), pp. 7–15. http://dx.doi.org/10.1007/BF03024783[Crossref]
  • [7] J.P. Ward: Quaternions and Cayley Numbers, Kluwer, London, 1996.
  • [8] K. Gürlebeck, W. Sprössig: Quaternionic and Clifford Calculus for Physicists and Engineers, Wiley & Sons, Chichester, 1997.
  • [9] P.R. Girard: “The quaternion group and modern physics”, Eur. J. Phys., Vol. 5, (1984), pp. 25–32. http://dx.doi.org/10.1088/0143-0807/5/1/007[Crossref]
  • [10] V.V. Kassandrov: “Biquaternionic electrodynamics and Weyl-Cartan geometry of space-time”, Grav. & Cosm., Vol. 3, (1995), pp. 216–222.
  • [11] W.E. Baylis: Electrodynamics: A Modern Geometric Approach, Birkhäuser, Boston, 1999.
  • [12] A. Waser: On the Notation of Maxwell’s Field Equation, (2000), http://www.info.global-scaling-verein.de/EssaysE.htm
  • [13] A. Waser: Quaternions in Electrodynamics, (2001), http://www.info.global-scaling-verein.de/EssaysE.htm
  • [14] A. Gsponer and J.P. Hurni: “Comments on formulating and generalizing Dirac’s, Proca’s, and Maxwell’s equations with biquaternions or Clifford numbers”, Found. Phys. Lett., Vol. 14, (2001), pp. 77–85. http://dx.doi.org/10.1023/A:1012033412964[Crossref]
  • [15] V.V. Kravchenko: “On a quaternionic reformulation of Maxwell’s equations for inhomogeneous media and new solutions”, Z. f. Anal.u. ihre Anwend., Vol. 21, (2002), pp. 21–26. [Crossref]
  • [16] V.V. Kravchenko: “On the relation between the Maxwell system and the Dirac equation”, Preprint: arXiv:math-ph/0202009.
  • [17] K. J. Van Vlaenderen and A. Waser: “Electrodynamics with the scalar field”, Hadronic J., Vol. 27, (2004), pp. 673–691
  • [18] S.M. Grudsky, K.V. Khmelnytskaya and V.V. Kravchenko: “On a quaternionic Maxwell equation for the timedependent electromagnetic field in a chiral medium”, J. Phys. A-Math. Gen., Vol. 37, (2004), pp. 4641–4647. http://dx.doi.org/10.1088/0305-4470/37/16/013[Crossref]
  • [19] D.H. Gottlieb: “Maxwell’s Equations”, Preprint: arXiv:math-ph/0409001.
  • [20] M. Tanışh: “Gauge transformation and electromagnetism with biquaternions”, Europhys. Lett., Vol. 74, (2006), pp. 569–573. http://dx.doi.org/10.1209/epl/i2005-10571-6[Crossref]
  • [21] O.P.S. Negi, S. Bisht and P.S. Bisht: “Revisiting quaternion formulation and electromagnetism”, Nuovo Cimento, Vol. 113, (1998), pp. 1449–1467.
  • [22] T. Tolan, K. Özdaş and M. Tanışh: “Reformulation of electromagnetism with octonions”, Nuovo Cimento B, Vol. 121B, (2006), pp. 43–55.
  • [23] M. Gogberashvili: “Octonionic electrodynamics”, J. Phys. A-Math. Gen., Vol. 39, (2006), pp. 7099–7104. http://dx.doi.org/10.1088/0305-4470/39/22/020[Crossref]
  • [24] P.S. Bisht and O.P.S. Negi: “Split octonion electrodynamics”, Indian J. Pure and Appl. Phys., Vol. 31, (1993), pp. 292–296.
  • [25] P.S. Bisht, S. Dangwal and O.P. Negi: “Unified Split Octonion Formulation of Dyons”, Preprint: arXiv:hep-th/0607209. [WoS]
  • [26] A.M. Frydryszak: “Dual numbers and supersymmetric mechanics”, Czech. J. Phys., Vol. 55, (2005), pp. 1409–1414; and references therein. http://dx.doi.org/10.1007/s10582-006-0018-5[Crossref]
  • [27] V. Majernik: “Quaternion formulation of the Galilean space-time transformation”, Acta Phys. Slovaca, Vol. 46, (2006), pp. 9–14.
  • [28] S. Demir and K. Özdaş: “Dual quaternionic reformulation of classical electromagnetism”, Acta Phys. Slovaca, Vol. 53, (2003), pp. 429–436.
  • [29] W. K. Clifford: “Preliminary Sketch of Biquaternions”, Proc. London Math. Soc., Vol. 4, (1873), pp. 381–395. http://dx.doi.org/10.1112/plms/s1-4.1.381[Crossref]
  • [30] A.E. Samuel, P.R. McAree and K.H. Hunt: “Unifying screw geometry and matrix transformations”, Int. J. Robot. Res., Vol. 10, (1991), pp. 454–472. http://dx.doi.org/10.1177/027836499101000502[Crossref]
  • [31] R. Horaud and F. Dornaika: “Hand-eye calibration”, Int. J. Robot. Res., Vol. 14, (1995), pp. 195–210. http://dx.doi.org/10.1177/027836499501400301[Crossref]
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-007-0031-8
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