Octonion symmetric Dirac--Maxwell equations

Chanyal, B. C.

doi:10.3906/fiz-1401-14

Cited by 17 publications

(3 citation statements)

References 37 publications

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“…The solution of (67) can be written as � = ϒexp(-mc 2 t/ħ), where ϒ satisfies the Klein-Gordon equation. Similarly, comparing scalar equations (22), (45) and (23), (45), we obtain the following quantum wave equations for dyonic scalar potentials �� e � m �:…”

Section: Quantum Structure For the Electromagnetic Wave Propagation Omentioning

confidence: 99%

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A relativistic quantum theory of dyons wave propagation

Chanyal

2017

Can. J. Phys.

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Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the electric and magnetic charge of dyons. We also demonstrate the universal quantum wave equations for two four-potentials as well as two four-currents of dyons. The generalized continuity equations for massive dyons in case of quantum fields are expressed. Furthermore, we concluded that the quantum generalization of electromagnetic field equations of dyons can be related to analogous London field equations (i.e., current to electromagnetic fields in and around a superconductor).Comment: 8 pages. arXiv admin note: text overlap with arXiv:hep-th/0608164 by other author

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Section: Quantum Structure For the Electromagnetic Wave Propagation Omentioning

confidence: 99%

“…where V ¡ (A + iB) and � ¡ �� e � i� m � are vector and scalar potentials of the dyon [22]. Moreover, the classical field equations of dyons and its conservation laws have already been discussed [23][24][25][26][27].…”

Section: Quantum Wave Propagation In An External Electromagnetic Fielmentioning

confidence: 99%

A relativistic quantum theory of dyons wave propagation

Chanyal

2017

Can. J. Phys.

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“…We find interesting superposition properties of memristor wave, which was studied inRefs. [37][38][39][40][41]47].…”

Section: Hmentioning

confidence: 99%

E. Cartan’s and A. Connnes’ Supersymmetry and Differences of Understanding Physical Phenomena

Furui¹

2018

JMSS

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Einstein claimed that one cannot define global time, and proposed defining local time additionally. Such approach was adopted also by E. Cartan, in which fermions are described by spinors with 16 bases and interact with vectors with 8 bases, that consists of a couple of 4 dimensional vectors x i (i = 1, ···, 4) and x i (i = 1, ···, 4). In Cartan's theory, spinors and vectors transform by super symmetric transformations G 23 , G 12 , G 13 , G 123 and G 132 and bases of fermion spinors consist of ξ 0 ,ξ i (i = 1, ···, 4), ξ 1234 , ξ 234 , ξ 134 , ξ 124 , ξ 123 and ξ i,j (i /= j ∈{1,2,3,4}). Except G 23 , the transformations mix spinors and vectors, and operations of G 23 on spinors contain G 23 ξ 4 = ξ 0 and G 23 ξ 123 = ξ 1234 , and operations of G 23 on vectors contain G 23 x 4 = −x 4' and G 23 x 4' = −x 4 . Therefore, there are 14 independent spinor bases and 7 independent vector bases, which corresponds to the number of bases of the G 2 symmetry.From the bases of non-commutative geometry, Connes took two fibers from a point of S 3 basis, and on top of fibers allowed two times propagate following von Neumann algebra, but evolution of the system was assumed to be defined by one-parameter group of transformation. Steenrod stated that the S 7 symmetry can be regarded as S 3 symmetry covered over S 4 symmetry, which allows decomposition of S

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Octonionic Gravi-Electromagnetism and Dark Matter

2015

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An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion algebra and its properties, we have discussed the octonionic unified gauge formulation for SU (2) × U (1) electroweak theory and SU (3) × SU (2) × U (1) grand unified theory. Describing the octonion eight dimensional space as the combination of two quaternionic spaces (namely associated with the electromagnetic interaction (EM-space) and linear gravitational interaction (G-space)), we have reexamined the unified picture of EM-G space in terms of octonionic split formulation in consistent manner. Consequently, we have obtained the various field equations for unified gravi-electromagnetic interactions. Furthermore, we have reconstructed the field equations of hot and cold dark matter in terms of split octonions. It is shown that the difference between the octonion cold dark matter (OCDM) and the octonion hot dark matter (OHDM) is significant in the formulating of structure of these two, because the velocities of octonion hot dark matter cause it to wipe out structure on small scales.

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Octonion symmetric Dirac--Maxwell equations

Cited by 17 publications

References 37 publications

A relativistic quantum theory of dyons wave propagation

A relativistic quantum theory of dyons wave propagation

E. Cartan’s and A. Connnes’ Supersymmetry and Differences of Understanding Physical Phenomena

Octonionic Gravi-Electromagnetism and Dark Matter

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