Reconstruction of symmetric Dirac–Maxwell equations using nonassociative algebra

Kalauni, Pushpa; Barata, João C. A.

doi:10.1142/s0219887815500292

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…Chanyal [17] et al described the octonion formulation of Abelian/non-Abelian gauge theory in terms of the Zorn vector matrix realization. Kalauni [18] et al obtained the fully symmetric Dirac-Maxwell's equations as one single equation by using the matrix presentation, with the help of the algebraic properties of quaternions and octonions.…”

Section: Existing Studiesmentioning

confidence: 99%

Forces in the complex octonion curved space

Weng

2016

Int. J. Geom. Methods Mod. Phys.

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The paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe the electromagnetic theory. It inspires subsequent scholars to study the electromagnetic and gravitational theories with the complex quaternions/octonions. Furthermore Einstein was the first to depict the gravitational theory by means of tensor analysis and curved four-space-time. Nowadays some scholars investigate the electromagnetic and gravitational properties making use of the complex quaternion/octonion curved space. From the orthogonality of two complex quaternions, it is possible to define the covariant derivative of the complex quaternion curved space, describing the gravitational properties in the complex quaternion curved space. Further it is possible to define the covariant derivative of the complex octonion curved space by means of the orthogonality of two complex octonions, depicting simultaneously the electromagnetic and gravitational properties in the complex octonion curved space. The result reveals that the connection coefficient and curvature of the complex octonion curved space will exert an influence on the field strength and field source of the electromagnetic and gravitational fields, impacting the linear momentum, angular momentum, torque, energy, and force and so forth.Comment: 27 page

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Section: Existing Studiesmentioning

confidence: 99%

Forces in the complex octonion curved space

Weng

2016

Int. J. Geom. Methods Mod. Phys.

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“…Rotation R 12 yields three simultaneous rotations by an angle 2θ in three planes (1,2), (5,4) and (6,7) and leaves x 3 unchanged. The above transformations of x under R 12 can be written as…”

Section: Role Of Division Algebra In Seven-dimensional Gauge Theorymentioning

confidence: 99%

“…(19), J 3 is 7 × 7 matrix which represents rotation around the x 3 axis or in the (1, 2), (5,4) and (6,7) planes, and it can be written as…”

Section: Generators For So(7) Groupmentioning

confidence: 99%

Role of division algebra in seven-dimensional gauge theory

Kalauni

Barata

2015

Mod. Phys. Lett. A

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The algebra of octonions O forms the largest normed division algebra over the real numbers R, complex numbers C and quaternions H. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang-Mills theory and field equation in seven-dimensional space.

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“…However, even though the color charge was deemed as one species of the physical substance, the QCD and assumed the dark matter may be able to be interpreted as matter emitting photons in a different triality sector, rather than that of electromagnetic probes in the world. With the help of the algebraic properties of quaternions and octonions, Kalauni et al [50] obtained the fully symmetric Dirac-Maxwell's equations as one single equation. Negi et al [51] applied the octonion to express the consistent form of generalized Maxwells equations in presence of electric and magnetic charges (dyons).…”

Section: Introductionmentioning

confidence: 99%

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

Weng¹

2017

Advances in Mathematical Physics

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The paper aims to apply the complex-sedenions to explore the wavefunctions and field equations of non-Abelian gauge fields, considering the spatial dimensions of a unit vector as the color degrees of freedom in the complex-quaternion wavefunctions, exploring the physical properties of the color confinement essentially. J. C. Maxwell was the first to employ the quaternions to study the physical properties of electromagnetic fields. His method inspires some subsequent scholars to introduce the quaternions, octonions, and sedenions to research the electromagnetic field, gravitational field, nuclear field, quantum mechanics, and gauge field. The application of complex-sedenions is capable of depicting not only the field equations of the classical mechanics on the macroscopic scale, but also the field equations of the quantum mechanics on the microscopic scale. The latter can be degenerated into the Dirac equation and Yang-Mills equation. In contrast to the complex-number wavefunction, the wavefunction in the complex-quaternion space possesses three new degrees of freedom, that is, three color degrees of freedom. One complex-quaternion wavefunction is equivalent to three conventional wavefunctions with the complex-numbers. It means that the three spatial dimensions of unit vector in the complex-quaternion wavefunction can be considered as the 'three colors', naturally the color confinement will be effective. In other words, in the complex-quaternion space, the 'three colors' are only the spatial dimensions, rather than any property of physical substance. The existing 'three colors' can be merged into the wavefunction, described with the complex-quaternions.other existing theories are still unable to account for the color confinement, laying themselves open to suspicion. The assumption of color charge in the QCD is appealing for more validation experiments. Up to now, the QCD may not be really perfect yet, especially its fundamental assumption. c) Dark matter. The existence of the physical phenomena connected with the dark matters was firstly validated in the astronomy, and then was accepted generally by the whole academic circle. Nevertheless the Standard Model is blind to the existence of dark matters, and it is unable to elucidate the relevant physical phenomena either. Further the Standard Model and even the 'Beyond the Standard Model' are incapable of predicting or inferring the confirmed dark matters. It means that the research scope, in the mainstream of current unification theories, is restricted and insufficient enough. For the unification theory, which is unable to explore the dark matter, there may be still something left to be improved. Apparently an appropriate unification theory must be capable of comprising and exploring the ordinary matter and dark matter simultaneously.Presenting a striking contrast to the above is that it is able to account for a few problems, derived from the QCD and other existing theories, in the quantum mechanics described with the complex-sedenions, trying to improve the unificat...

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Reconstruction of symmetric Dirac–Maxwell equations using nonassociative algebra

Cited by 4 publications

References 21 publications

Forces in the complex octonion curved space

Forces in the complex octonion curved space

Role of division algebra in seven-dimensional gauge theory

Color Confinement and Spatial Dimensions in the Complex-Sedenion Space

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