跳至主要内容

Associative Space-Time Sedenions and Their Application in Relativistic Quantum Mechanics and Field Theory

Read  full  paper  at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=52976#.VK8sqMnQrzE

Author(s)   
 
ABSTRACT
We present an alternative sixteen-component hypercomplex scalar-vector values named “space-time sedenions”, generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quantum mechanics and field theory equations based on sedenionic wave function and space-time operators is discussed.
 
Cite this paper
Mironov, V. and Mironov, S. (2015) Associative Space-Time Sedenions and Their Application in Relativistic Quantum Mechanics and Field Theory. Applied Mathematics, 6, 46-56. doi: 10.4236/am.2015.61006.
 
References
[1]Adler, S.L. (1995) Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, New York.
 
[2]Imaeda, K. (1976) A New Formulation of Classical Electrodynamics. Nuovocimento, 32, 138-162.
http://dx.doi.org/10.1007/BF02726749
 
[3]Majernik, V. (1999) Quaternionic Formulation of the Classical Fields. Advances in Applied Clifford Algebras, 9, 119-130.
http://dx.doi.org/10.1007/BF03041944
 
[4]Davies, A.J. (1990) Quaternionic Dirac Equation. Physical Review D, 41, 2628-2630.
http://dx.doi.org/10.1103/PhysRevD.41.2628
 
[5]Schwartz, C. (2006) Relativistic Quaternionic Wave Equation. Journal of Mathematical Physics, 47, Article ID: 122301.
http://dx.doi.org/10.1063/1.2397555
 
[6]Liu, Y.-F. (2002) Triality, Biquaternion and Vector Representation of the Dirac Equation. Advances in Applied Clifford Algebras, 12, 109-124.
http://dx.doi.org/10.1007/BF03161242
 
[7]Gogberashvili, M. (2006) Octonionic Electrodynamics. Journal of Physics A: Mathematics in General, 39, 7099-7104.
http://dx.doi.org/10.1088/0305-4470/39/22/020
 
[8]Gamba, A. (1998) Maxwell’s Equations in Octonion Form. NuovoCimento A, 111, 293-302.
 
[9]Tolan, T., ?zdas, K. and Tanisli, M. (2006) Reformulation of Electromagnetism with Octonions. Nuovo Cimento B, 121, 43-55.
http://dx.doi.org/10.1393/ncb/i2005-10189-9
 
[10]Gogberashvili, M. (2006) Octonionic Version of Dirac Equations. International Journal of Modern Physics A, 21, 3513-3523.
http://dx.doi.org/10.1142/S0217751X06028436
 
[11]De Leo, S. and Abdel-Khalek, K. (1996) Octonionic Dirac Equation. Progress in Theoretical Physics, 96, 833-846.
http://dx.doi.org/10.1143/PTP.96.833
 
[12]Dickson, L.E. (1919) On Quaternions and Their Generalization and the History of the Eight Square Theorem. Annals of Mathematics, 20, 155-171.
http://dx.doi.org/10.2307/1967865
 
[13]Imaeda, K. and Imaeda, M. (2000) Sedenions: Algebra and Analysis. Applied Mathematics and Computations, 115, 77-88.
http://dx.doi.org/10.1016/S0096-3003(99)00140-X
 
[14]Carmody, K. (1988) Circular and Hyperbolic Quaternions, Octonions, and Sedenions. Applied Mathematics and Computations, 28, 47-72.
http://dx.doi.org/10.1016/0096-3003(88)90133-6
 
[15]Carmody, K. (1997) Circular and Hyperbolic Quaternions, Octonions, and Sedenions—Further Results. Applied Mathematics and Computations, 84, 27-47.
http://dx.doi.org/10.1016/S0096-3003(96)00051-3
 
[16]K?plinger, J. (2006) Dirac Equation on Hyperbolic Octonions. Applied Mathematics and Computations, 182, 443-446.
http://dx.doi.org/10.1016/j.amc.2006.04.005
 
[17]Mironov, V.L. and Mironov, S.V. (2009) Octonic Representation of Electromagnetic Field Equations. Journal of Mathematical Physics, 50, Article ID: 012901.
http://dx.doi.org/10.1063/1.3041499
 
[18]Mironov, V.L. and Mironov, S.V. (2009) Octonic Second-Order Equations of Relativistic Quantum Mechanics. Journal of Mathematical Physics, 50, Article ID: 012302.
http://dx.doi.org/10.1142/S0217751X09045480
 
[19]Mironov, V.L. and Mironov, S.V. (2009) Octonic First-Order Equations of Relativistic Quantum Mechanics. International Journal of Modern Physics A, 24, 4157-4167.
http://dx.doi.org/10.1142/S0217751X09045480
 
[20]Mironov, V.L. and Mironov, S.V. (2011) Noncommutative Sedeons and Their Application in Field Theory. e-Print.
http://arxiv.org/abs/1111.4035
 
[21]Mironov, V.L. and Mironov, S.V. (2013) Reformulation of Relativistic Quantum Mechanics Equations with Non-Commutative Sedeons. Applied Mathematics, 4, 53-60.
http://dx.doi.org/10.4236/am.2013.410A3007
 
[22]Mironov, V.L. and Mironov, S.V. (2014) Sedeonic Equations of Gravitoelectromagnetism. Journal of Modern Physics, 5, 917-927.
http://dx.doi.org/10.4236/jmp.2014.510095
 
[23]Mironov, S.V. and Mironov, V.L. (2014) Sedeonic Equations of Massive Fields. International Journal of Theoretical Physics, e-Print.
http://vixra.org/abs/1311.0005
 
[24]Mironov, S.V. and Mironov, V.L. (2014) Space-Time Sedeons and Their Application in Relativistic Quantum Mechanics and Field Theory. Institute for Physics of Microstructures RAS, Nizhny Novgorod.
http://vixra.org/abs/1407.0068
 
[25]Landau, L.D. and Lifshits, E.M. (1975) Classical Theory of Fields. 4th Edition, Pergamon Press, New York.
 
[26]Dirac, P.A.M. (1958) The Principles of Quantum Mechanics. Clarendon Press, Oxford.
 
[27]Cafaro, C. and Ali, S.A. (2006) The Spacetime Algebra Approach to Massive Classical Electrodynamics with Magnetic Monopoles. Advances in Applied Clifford Algebras, 17, 23-36.
http://dx.doi.org/10.1007/s00006-006-0014-7
 
[28]Macfarlane, A. (1900) Hyperbolic Quaternions. Proceedings of the Royal Society at Edinburgh, 1899-1900 Session, 169-181.
 
[29]Hamilton, W.R. (1853) Lectures on Quaternions. Royal Irish Academy, Dublin.                   eww150109lx
标签：

评论

发表评论

此博客中的热门博文