Reformulation of Relativistic Quantum Mechanics Equations with Non-Commutative Sedeons

Show more

References

[1] S. L. Adler, “Quaternionic Quantum Mechanics and Quantum Fields,” Oxford University Press, New York, 1995.

[2] V. Majernik, “Quaternionic Formulation of the Classical Fields,” Advances in Applied Clifford Algebras, Vol. 9, No. 1, 1999, pp. 119-130.

http://dx.doi.org/10.1007/BF03041944

[3] K. Imaeda, “A New Formulation of Classical Electrodynamics,” Nuovo Cimento, Vol. 32, No. 1, 1976, pp. 138162. http://dx.doi.org/10.1007/BF02726749

[4] A. J. Davies, “Quaternionic Dirac Equation,” Physical Review D, Vol. 41, No. 8, 1990, pp. 2628-2630.

http://dx.doi.org/10.1103/PhysRevD.41.2628

[5] S. De Leo and P. Rotelli, “Quaternion Scalar Field,” Physical Review D, Vol. 45, No. 2, 1992, pp. 575-579.

http://dx.doi.org/10.1103/PhysRevD.45.575

[6] C. Schwartz, “Relativistic Quaternionic Wave Equation,” Journal of Mathematical Physics, Vol. 47, No. 12, 2006, Article ID: 122301. http://dx.doi.org/10.1063/1.2397555

[7] Y.-F. Liu, “Triality, Biquaternion and Vector Representation of the Dirac Equation,” Advances in Applied Clifford Algebras, Vol. 12, No. 2, 2002, pp. 109-124.

http://dx.doi.org/10.1007/BF03161242

[8] M. Gogberashvili, “Octonionic Electrodynamics,” Journal of Physics A: Mathematics in General, Vol. 39, No. 22, 2006, pp. 7099-7104.

http://dx.doi.org/10.1088/0305-4470/39/22/020

[9] A. Gamba, “Maxwell’s Equations in Octonion Form,” Nuovo Cimento A, Vol. 111, No. 3, 1998, pp. 293-302.

[10] T. Tolan, K. Ozdas and M. Tanisli, “Reformulation of Electromagnetism with Octonions,” II Nuovo Cimento B, Vol. 121, No. 1, 2006, pp. 43-55.

http://dx.doi.org/10.1393/ncb/i2005-10189-9

[11] S. Demir and M. Tanisli, “A Compact Biquaternionic Formulation of Massive Field Equations in Gravi-Electromagnetism,” European Physical Journal Plus, Vol. 126, 2011, p. 115.

http://dx.doi.org/10.1140/epjp/i2011-11115-8

[12] B. C. Chanyal, P. S. Bisht and O. P. S. Negi, “Generalized Octonion Electrodynamics,” International Journal of Theoretical Physics, Vol. 49, No. 6, 2010, pp. 1333-1343.

http://dx.doi.org/10.1007/s10773-010-0314-5

[13] P. S. Bisht, G. Karnatak and O. P. S. Negi, “Generalized Gravi-Electromagnetism,” International Journal of Theoretical Physics, Vol. 49, No. 6, 2010, pp. 1344-1356.

http://dx.doi.org/10.1007/s10773-010-0315-4

[14] V. Dzhunushaliev, “Nonassociativity, Supersymmetry and Hidden Variables,” Journal of Mathematical Physics, Vol. 49, No. 4, 2008, Article ID: 042108.

http://dx.doi.org/10.1063/1.2907868

[15] M. Gogberashvili, “Octonionic Version of Dirac Equations,” International Journal of Modern Physics A, Vol. 21, No. 17, 2006, pp. 3513-3523.

http://dx.doi.org/10.1142/S0217751X06028436

[16] S. De Leo and K. Abdel-Khalek, “Octonionic Dirac Equation,” Progress in Theoretical Physics, Vol. 96, No. 4, 1996, pp. 833-846.

http://dx.doi.org/10.1143/PTP.96.833

[17] D. Hestenes, “Observables, Operators, and Complex Numbers in the Dirac Theory,” Journal of Mathematical Physics, Vol. 16, No. 3, 1975, pp. 556-572.

http://dx.doi.org/10.1063/1.522554

[18] K. Imaeda and M. Imaeda, “Sedenions: Algebra and Analysis,” Applied Mathematics and Computations, Vol. 115, No. 2-3, 2000, pp. 77-88.

http://dx.doi.org/10.1016/S0096-3003(99)00140-X

[19] K. Carmody, “Circular and Hyperbolic Quaternions, Octonions, and Sedenions,” Applied Mathematics and Computations, Vol. 28, No. 1, 1988, pp. 47-72.

http://dx.doi.org/10.1016/0096-3003(88)90133-6

[20] K. Carmody, “Circular and Hyperbolic Quaternions, Octonions, and Sedenions—Further Results,” Applied Mathematics and Computations, Vol. 84, No. 1, 1997, pp. 27-47. http://dx.doi.org/10.1016/S0096-3003(96)00051-3

[21] J. Koplinger, “Dirac Equation on Hyperbolic Octonions,” Applied Mathematics and Computations, Vol. 182, No. 1, 2006, pp. 443-446.

http://dx.doi.org/10.1016/j.amc.2006.04.005

[22] S. Demir and M. Tanisli, “Sedenionic Formulation for Generalized Fields of Dyons,” International Journal of Theoretical Physics, Vol. 51, No. 4, 2012, pp. 1239-1252.

http://dx.doi.org/10.1007/s10773-011-0999-0

[23] W. P. Joyce, “Dirac Theory in Spacetime Algebra: I. The Generalized Bivector Dirac Equation,” Journal of Physics A: Mathematics in General, Vol. 34, No. 10, 2001, pp. 1991-2005.

http://dx.doi.org/10.1088/0305-4470/34/10/304

[24] C. Cafaro and S. A. Ali, “The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles,” Advances in Applied Clifford Algebras, Vol. 17, No. 1, 2006, pp. 23-36.

http://dx.doi.org/10.1007/s00006-006-0014-7

[25] V. L. Mironov and S. V. Mironov, “Octonic Representation of Electromagnetic Field Equations,” Journal of Mathematical Physics, Vol. 50, No. 1, 2009, Article ID: 012901. http://dx.doi.org/10.1063/1.3041499

[26] V. L. Mironov and S. V. Mironov, “Octonic SecondOrder Equations of Relativistic Quantum Mechanics,” Journal of Mathematical Physics, Vol. 50, No. 1, 2009, Article ID: 012302.

http://dx.doi.org/10.1063/1.3058644

[27] V. L. Mironov and S. V. Mironov, “Octonic First-Order Equations of Relativistic Quantum Mechanics,” International Journal of Modern Physics A, Vol. 24, No. 22, 2009, pp. 4157-4167.

http://dx.doi.org/10.1142/S0217751X09045480

[28] V. L. Mironov and S. V. Mironov, “Sedeonic Generalization of Relativistic Quantum Mechanics,” International Journal of Modern Physics A, Vol. 24, No. 32, 2009, pp. 6237-6254.

http://dx.doi.org/10.1142/S0217751X09047739

[29] L. D. Landau and E. M. Lifshits, “Classical Theory of Fields,” 4th Edition, Pergamon Press, New York, 1975.

[30] P. A. M. Dirac, “The Principles of Quantum Mechanics,” Clarendon Press, Oxford, 1958.

[31] A. Macfarlane, “Hyperbolic Quaternions,” Proceedings of the Royal Society at Edinburgh, 1899-1900 Sessions, pp. 169-181.

[32] W. Pauli, “Zur Quantenmechanik des Magnetischen Elektrons,” Zeitschrift für Physik, Vol. 43, No. 9-10, 1927, pp. 601-623. http://dx.doi.org/10.1007/BF01397326

[33] P. A. M. Dirac, “The Quantum Theory of the Electron,” Proceedings of Royal Society at London. Series A, Vol. 117, No. 778, 1928, pp. 610-624.

http://dx.doi.org/10.1098/rspa.1928.0023