Quaternion Gravi-Electromagnetism

Rawat, Ashish; Negi, O. P. S.

doi:10.1007/s10773-011-0953-1

Cited by 38 publications

(19 citation statements)

References 23 publications

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“…F. A. Doria 8 adopted the quaternion to research the gravitational theory. A. S. Rawat 9 etc discussed the gravitational field equation with the quaternion treatment. V. Majernik 10 studied the extended Maxwell-like gravitational field equations with the quaternion.…”

Section: Introductionmentioning

confidence: 99%

Angular momentum and torque described with the complex octonion

Weng

2014

AIP Advances

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The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum (or torque, force) to combine some physics contents, which were considered to be independent of each other in the past. J. C. Maxwell used simultaneously two methods, the vector terminology and quaternion analysis, to depict the electromagnetic theory. It motivates the paper to introduce the quaternion space into the field theory, describing the physical feature of electromagnetic and gravitational fields. The spaces of two fields can be chosen as the quaternion spaces, while the coordinate component of quaternion space is able to be the complex number. The quaternion space of electromagnetic field is independent of that of gravitational field. These two quaternion spaces may compose one octonion space. Contrarily, one octonion space can be separated into two subspaces, the quaternion space and S-quaternion space. In the quaternion space, it is able to infer the field potential, field strength, field source, angular momentum, torque, and force etc in the gravitational field. In the S-quaternion space, it is capable of deducing the field potential, field strength, field source, current continuity equation, and electric (or magnetic) dipolar moment etc in the electromagnetic field. The results reveal that the quaternion space is appropriate to describe the gravitational features, including the torque, force, and mass continuity equation etc. The S-quaternion space is proper to depict the electromagnetic features, including the dipolar moment and current continuity equation etc. In case the field strength is weak enough, the force and the continuity equation etc can be respectively reduced to that in the classical field theory.Comment: 11 pages, minor change

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Section: Introductionmentioning

confidence: 99%

Angular momentum and torque described with the complex octonion

Weng

2014

AIP Advances

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“…Correspondingly, the angular momentum solutions for rotating Dirac anti-particle, we take Ψ 2 = 1 and Ψ 3 = 0 for spin up state and Ψ 2 = 0 and Ψ 3 = 1 for spin down states, then 13) where…”

Section: One Component Solutionsmentioning

confidence: 99%

A comparative study of quaternionic rotational Dirac equation and its interpretation

Chanyal¹,

Sandhya²

2020

Int. J. Geom. Methods Mod. Phys.

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In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists the rotational energy and angular momentum of particle and anti-particle. Accordingly, we also discuss the four vector form of quaternionic relativistic mass, moment of inertia and rotational energy-momentum in Euclidean space-time. The quaternionic four angular momentum (i.e. the rotational analogy of four linear momentum) predicts the dual energy (rest mass energy and pure rotational energy) and dual momentum (linear like momentum and pure rotational momentum). Further, the solutions of quaternionic rotational Dirac energy-momentum are obtained by using one, two and fourcomponent of quaternionic spinor. We also demonstrate the solutions of quaternionic plane wave equation which gives the rotational frequency and wave propagation vector of Dirac particles and anti-particles in terms of quaternionic form. PACS: 03.65.−w, 03.65.Fd, 02.10.Ud relativistic velocity. To combine the special theory of relativity with quantum mechanics, there has been developed the relativistic quantum mechanics. In the same way, Klein-Gordon and Dirac independently investigated the relativistic wave equations by combining special relativity with quantum mechanics. These relativistic wave equations describe the various phenomenons that occur in high energy physics and are invariant under Lorentz transformations. Dirac [1] discussed a relativistic quantum wave equation by using Hamiltonian operator to overcome the difficulties arising in Klein-Gordon equation. As we know that the conservation of energy and angular momentum are one of the mandatory conservation laws to check the validity of Dirac particles. Keeping in mind the conservation laws of energy and angular momentum of a rotating particle, in this paper, we proposed a quaternionic Dirac equation that consists not only the energy representation but also shows the angular momentum representation of spin-1/2 particles. The quaternion number [2] is basically an extension of complex numbers. Although, there are four types of norm-division algebras, i.e. real, complex, quaternion and octonion algebra. The division algebra is defined as an algebra in which all non-zero elements have their inverse under multiplication [3]. Nowadays, the quaternionic algebra is a popular algebra to study the various theories in modern theoretical physics. The quaternionic algebra is associative and commutative under addition but not commutative under multiplication. Thus, this algebra form a group under multiplication but not an Abelian group, is also called the division ring. Many researchers have attempted the formulation of usual Dirac equation for free particles in terms of quaternionic algebra. Firstly, Rotelli [4] developed the Dirac equation in quaternionic four fields. The another version of quaternionic Dirac equation has been studied by Rawat et. al [5] with the description of quaternionic spinor...

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“…Negi et al [9][10][11][12][13][14] have discussed the quaternionic formulations in different areas of physics for unified theory of linear gravity and electromagnetism with the simultaneous existence of electric, magnetic, gravitational and Heavisidean charges (masses). Similarly, Demir and co-workers 15 have derived the quaternionic representation of Klein-Gordon equation for the particle carrying both electromagnetic and gravitational charges simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Octonic massless field equations

Demir

Tanışlı

Kansu

2015

Int. J. Mod. Phys. A

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In this paper, it is proven that the associative octons including scalar, pseudoscalar, pseudovector and vector values are convenient and capable tools to generalize the Maxwell-Dirac like field equations of electromagnetism and linear gravity in a compact and simple way. Although an attempt to describe the massless field equations of electromagnetism and linear gravity needs the sixteen real component mathematical structures, it is proved that these equations can be formulated in terms of eight components of octons. Furthermore, the generalized wave equation in terms of potentials is derived in the presence of electromagnetic and gravitational charges (masses). Finally, conservation of energy concept has also been investigated for massless fields.

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Quaternion Gravi-Electromagnetism

Abstract: Defining the generalized charge, potential, current and generalized fields as complex quantities where real and imaginary parts represent gravitation and electromagnetism respectively,

Cited by 38 publications

References 23 publications

Angular momentum and torque described with the complex octonion

Angular momentum and torque described with the complex octonion

A comparative study of quaternionic rotational Dirac equation and its interpretation

Octonic massless field equations

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