Octonion form of duality-invariant field equations for dyons
Yıl: 2020 Cilt: 44 Sayı: 1 Sayfa Aralığı: 10 - 23 Metin Dili: İngilizce DOI: 10.3906/fiz-1910-7 İndeks Tarihi: 04-05-2020
Octonion form of duality-invariant field equations for dyons
Öz: The hypothetical particles dyons, which carry both electric and magnetic charges simultaneously, are widelydiscussed in application to electromagnetic theory and magnetohydrodynamics. Particularly, the duality-invariant fieldequations were suggested with suitable definitions of the dyon’s electromagnetic characteristics. In this study, we proposean alternative formulation of the duality-invariant field equations for dyons based on octonion algebra. Octonions havebeen used to express the equations for potentials, field strengths, and sources in a more compact and consistent manner.Additionally, the octonionic form of the energy conservation law for dyons has been derived.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- 1] Schwinger J. Magnetic charge and quantum field theory. Physical Review Journals 1966; 144 (4): 1087-1093. doi: 10.1103/PhysRev.144.1087
- [2] Negi OPS, Dehnen H, Karnatak G, Bisht PS. Generalization of Schwinger-Zwanziger dyon to quaternion. International Journal of Theoretical Physics 2011; 50 (6): 1908-1918. doi: 10.1007/s10773-011-0705-2
- [3] Bisht PS, Pushpa, Negi OPS. Magnetohydrodynamics in presence of electric and magnetic charges. Communications in Physics 2012; 22 (2): 111-124. doi: 10.15625/0868-3166/22/2/180
- [4] Coceal O, Sabra WA, Thomas S. Duality-invariant magnetohydrodynamics and dyons. Europhysics Letters 1996; 35 (4): 277-282. doi: 10.1209/epl/i1996-00566-9
- [5] Coceal O, Sabra WA, Thomas S. Conformal solutions of duality-invariant 2d magnetohydrodynamic turbulence. Europhysics Letters 1996; 35 (5): 343-348. doi: 10.1209/epl/i1996-00117-6
- [6] Coceal O, Sabra WA, Thomas S. Strings and dyonic plasmas. Physics Letters B 1996; 389 (4): 655-660. doi:10.1016/S0370-2693(96)80005-0
- [7] Bisht PS, Dangwal S, Negi OPS. Unified split octonion formulation of dyons. International Journal of Theoretical Physics 2008; 47 (9): 2297-2313. doi: 10.1007/s10773-008-9662-9
- [8] Dehnen H, Negi OPS. Electromagnetic duality, quaternion and supersymmetric gauge theories of dyons. arXiv hep-th/0608164v1, 2006.
- [9] Negi OPS, Dehnen H. Gauge formulation for two potential theory of dyons. International Journal of Theoretical Physics 2011; 50 (8): 2446-2459. doi: 10.1007/s10773-011-0733-y
- [10] Bisht PS, Negi OPS. Revisiting quaternion dual electrodynamics. International Journal of Theoretical Physics 2008, 47 (12): 3108-3120. doi: 10.1007/s10773-008-9744-8
- [11] Olesen P. Dual strings and magnetohydrodynamics. Physics Letters B 1996; 366 (1-4): 117-123. doi: 10.1016/0370- 2693(95)01383-0
- [12] Gamba A. Maxwell’s equations in octonion form. Nuovo Cimento A 1998; 111 (3): 293-302.
- [13] Davies AJ. Quaternionic Dirac equation. Physical Review D 1990; 41 (8): 2628-2630. doi: 10.1103/Phys- RevD.41.2628
- [14] Tanışlı M. Gauge transformation and electromagnetism with biquaternions. Europhysics Letters 2006; 74 (4): 569- 574. doi: 10.1209/epl/i2005-10571-6
- [15] Tanışlı M, Kansu ME, Demir S. A new approach to Lorentz invariance in electromagnetism with hyperbolic octonions. European Physical Journal Plus 2012; 127 (6): 69. doi: 10.1140/epjp/i2012-12069-y
- [16] Tanışlı M, Kansu ME. Octonionic Maxwell’s equations for bi-isotropic media. Journal of Mathematical Physics 2011; 52 (5): 053511. doi: 10.1063/1.3582816
- [17] Kansu ME, Tanışlı M, Demir S. Electromagnetic energy conservation with complex octonions. Turkish Journal of Physics 2012; 36 (3): 438-445. doi: 10.3906/fiz-1109-18
- [18] Kansu ME, Tanışlı M, Demir S. Representation of electromagnetic and gravitoelectromagnetic Poynting theorems in higher dimensions. Turkish Journal of Physics 2014; 38 (2): 155-164. doi: 10.3906/fiz-1311-13
- [19] Tanışlı M, Kansu ME, Demir S. Reformulation of electromagnetic and gravito-electromagnetic equations for Lorentz system with octonion algebra. General Relativity and Gravitation 2014; 46 (5): 1739. doi: 10.1007/s10714-014-1739- 6
- [20] Tolan T, Özdaş K, Tanışlı M. Reformulation of electromagnetism with octonions. Nuovo Cimento B 2006; 121 (1): 43-55. doi: 10.1393/ncb/i2005-10189-9
- [21] Candemir N, Tanışlı M, Özdaş K, Demir S. Hyperbolic octonionic Proca-Maxwell equations. Zeitschrift für Naturforschung A 2008; 63 (1-22): 15-18. doi: 10.1515/zna-2008-1-203
- [22] Demir S, Tanışlı M. Sedenionic formulation for generalized fields of dyons. International Journal of Theoretical Physics 2012; 51 (4): 1239-1252. doi: 10.1007/s10773-011-0999-0
- [23] Demir S, Tanışlı M. Biquaternionic Proca-type generalization of gravity. European Physical Journal Plus 2011; 126 (5): 51. doi: 10.1140/epjp/i2011-11051-7
- [24] Demir S, Tanışlı M. A compact biquaternionic formulation of massive field equations in gravi-electromagnetism. European Physical Journal Plus 2011; 126 (11): 115. doi: 10.1140/epjp/i2011-11115-8
- [25] Demir S, Tanışlı M, Kansu ME. Generalized hyperbolic octonion formulation for the fields of massive dyons and gravito-dyons. International Journal of Theoretical Physics 2013; 52 (10): 3696-3713. doi: 10.1007/s10773-013-1675- 3
- [26] Demir S, Tanışlı M, Kansu ME. Octonic massless field equations. International Journal of Modern Physics A 2015; 30 (15): 1550084. doi: 10.1142/S0217751X15500840
- [27] Demir S, Kekeç S. Octonic massive field equations. International Journal of Theoretical Physics 2016; 55 (7): 3338-3352. doi: 10.1007/s10773-016-2963-5
- [28] Demir S, Tanışlı M. Hyperbolic octonion formulation of the fluid Maxwell equations. Journal of the Korean Physical Society 2016; 68 (5): 616-623. doi: 10.3938/jkps.68.616
- [29] Köplinger J. Gravity and electromagnetism on conic sedenions. Applied Mathematics and Computation 2007; 188 (1): 948-953. doi: 10.1016/j.amc.2006.10.050
- [30] Köplinger J. Dirac equation on hyperbolic octonions. Applied Mathematics and Computation 2006; 182 (1): 443-446. doi: 10.1016/j.amc.2006.04.005
- [31] Kravchenko VV. Quaternionic reformulation of Maxwell’s equations for inhomogeneous media and new solutions. Zeitschrift für Analysis und ihre Anwendungen 2002; 21 (1): 21-26. doi: 10.4171/ZAA/1063
- [32] Grudsky MS, Khmelnytskaya KV, Kravchenko VV. On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium. Journal of Physics A 2004; 37 (16): 4641-4647. doi: 10.1088/0305- 4470/37/16/013
- [33] Mironov VL, Mironov SV. Octonic representation of electromagnetic field equations. Journal of Mathematical Physics 2009; 50 (1): 012901. doi: 10.1063/1.3041499
- [34] Mironov VL, Mironov SV. Sedeonic generalization of relativistic quantum mechanics. International Journal of Modern Physics A 2009; 24 (32): 6237-6254. doi: 10.1142/S0217751X09047739
- [35] Mironov VL, Mironov SV. Reformulation of relativistic quantum mechanics equations with non-commutative sedeons. Applied Mathematics 2013; 4 (10C): 53-60. doi: 10.4236/am.2013.410A3007
- [36] Mironov VL, Mironov SV. Sedeonic equations of gravitoelectromagnetism. Journal of Modern Physics 2014; 5 (10): 917-927. doi: 10.4236/jmp.2014.510095
- [37] Mironov VL, Mironov SV. Associative space-time sedenions and their application in relativistic quantum mechanics and field theory. Applied Mathematics 2015; 6 (1): 46-56. doi: 10.4236/am.2015.61006
- [38] Mironov VL, Mironov SV. Sedeonic field equations for dyons. Advances in Applied Clifford Algebras 2018; 28 (3): 64. doi: 0.1007/s00006-018-0886-3
- [39] Chanyal BC, Bisht PS, Negi OPS. Generalized octonion electrodynamics. International Journal of Theoretical Physics 2010; 49 (6): 1333-1343. doi: 10.1007/s10773-010-0314-5
- [40] Chanyal BC, Bisht PS, Negi OPS. Generalized split-octonion electrodynamics. International Journal of Theoretical Physics 2011; 50 (6): 1919-1926. doi: 10.1007/s10773-011-0706-1
- [41] Chanyal BC, Sharma VK, Negi OPS. Octonionic gravi-electromagnetism and dark matter. International Journal of Theoretical Physics 2015; 54 (10): 3516-3532. doi: 10.1007/s10773-015-2595-1
- [42] Chanyal BC. Sedenion unified theory of gravi-electromagnetism. Indian Journal of Physics 2014; 88 (11): 1197-1205. doi: 10.1007/s12648-014-0562-y
- [43] Chanyal BC. Dual octonion electrodynamics with the massive field of dyons. Journal of Mathematical Physics 2016; 57 (3): 033503. doi: 10.1063/1.4943594
- [44] Chanyal BC, Chanyal SK. Dual number coefficient octonion algebra, field equations and conservation laws. Analysis and Mathematical Physics 2017; 7 (3): 319-334. doi: 10.1007/s13324-016-0144-6
- [45] Chanyal BC, Chanyal SK, Bektaş Ö, Yüce S. A new approach on electromagnetism with dual number coefficient octonion algebra. International Journal of Geometric Methods in Modern Physics 2016; 13 (9): 1630013. doi: 10.1142/S0219887816300130
- [46] Bisht PS, Negi OPS. Quaternion-octonion analyticity for abelian and non-abelian gauge theories of dyons. International Journal of Theoretical Physics 2008; 47 (6): 1497-1511. doi: 10.1007/s10773-007-9591-z
- [47] Rawat S, Negi OPS. Quaternionic formulation of supersymmetric quantum mechanics. International Journal of Theoretical Physics 2009; 48 (2): 305-314. doi: 10.1007/s10773-008-9803-1
- [48] Rawat S, Negi OPS. Quaternion Dirac equation and supersymmetry. International Journal of Theoretical Physics 2009; 48 (8): 2222-2234. doi: 10.1007/s10773-009-0003-4
- [49] Okubo S. Introduction to Octonion and Other Non-associative Algebras in Physics. Cambridge, UK: Cambridge University Press, 1995.
- [50] Baez JC. The octonions. Bulletin of the American Mathematical Society 2002; 39 (2): 145-205. doi: 10.1090/S0273- 0979-01-00934-X
- [51] Jackson JD. Classical Electrodynamics. 3rd ed. New York, NY, USA: Wiley, 1999.
- [52] Dirac PAM. Quantised singularities in the electromagnetic field. Proceedings of the Royal Society A 1931; 133 (821): 60-72. doi: 10.1098/rspa.1931.0130 [53] Dirac PAM. The theory of magnetic poles. Physical Review Journals 1948; 74 (7): 817-830. doi: 10.1103/Phys- Rev.74.817
APA | Kansu M, TANIŞLI M, DEMİR S (2020). Octonion form of duality-invariant field equations for dyons. , 10 - 23. 10.3906/fiz-1910-7 |
Chicago | Kansu Mustafa Emre,TANIŞLI MURAT,DEMİR Süleyman Octonion form of duality-invariant field equations for dyons. (2020): 10 - 23. 10.3906/fiz-1910-7 |
MLA | Kansu Mustafa Emre,TANIŞLI MURAT,DEMİR Süleyman Octonion form of duality-invariant field equations for dyons. , 2020, ss.10 - 23. 10.3906/fiz-1910-7 |
AMA | Kansu M,TANIŞLI M,DEMİR S Octonion form of duality-invariant field equations for dyons. . 2020; 10 - 23. 10.3906/fiz-1910-7 |
Vancouver | Kansu M,TANIŞLI M,DEMİR S Octonion form of duality-invariant field equations for dyons. . 2020; 10 - 23. 10.3906/fiz-1910-7 |
IEEE | Kansu M,TANIŞLI M,DEMİR S "Octonion form of duality-invariant field equations for dyons." , ss.10 - 23, 2020. 10.3906/fiz-1910-7 |
ISNAD | Kansu, Mustafa Emre vd. "Octonion form of duality-invariant field equations for dyons". (2020), 10-23. https://doi.org/10.3906/fiz-1910-7 |
APA | Kansu M, TANIŞLI M, DEMİR S (2020). Octonion form of duality-invariant field equations for dyons. Turkish Journal of Physics, 44(1), 10 - 23. 10.3906/fiz-1910-7 |
Chicago | Kansu Mustafa Emre,TANIŞLI MURAT,DEMİR Süleyman Octonion form of duality-invariant field equations for dyons. Turkish Journal of Physics 44, no.1 (2020): 10 - 23. 10.3906/fiz-1910-7 |
MLA | Kansu Mustafa Emre,TANIŞLI MURAT,DEMİR Süleyman Octonion form of duality-invariant field equations for dyons. Turkish Journal of Physics, vol.44, no.1, 2020, ss.10 - 23. 10.3906/fiz-1910-7 |
AMA | Kansu M,TANIŞLI M,DEMİR S Octonion form of duality-invariant field equations for dyons. Turkish Journal of Physics. 2020; 44(1): 10 - 23. 10.3906/fiz-1910-7 |
Vancouver | Kansu M,TANIŞLI M,DEMİR S Octonion form of duality-invariant field equations for dyons. Turkish Journal of Physics. 2020; 44(1): 10 - 23. 10.3906/fiz-1910-7 |
IEEE | Kansu M,TANIŞLI M,DEMİR S "Octonion form of duality-invariant field equations for dyons." Turkish Journal of Physics, 44, ss.10 - 23, 2020. 10.3906/fiz-1910-7 |
ISNAD | Kansu, Mustafa Emre vd. "Octonion form of duality-invariant field equations for dyons". Turkish Journal of Physics 44/1 (2020), 10-23. https://doi.org/10.3906/fiz-1910-7 |