Quaternionic Approach to Dual Magnetohydrodynamics of Dyonic Cold Plasma

Chanyal, B. C.; Pathak, Mayank

doi:10.1155/2018/7843730

Cited by 21 publications

(8 citation statements)

References 48 publications

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“…In MHD, the simplest system for macroscopic transport equations of fluid plasma is known as the cold plasma model. We introduce the following approximation of fluid parameters to the case of cold plasma [15,16,17] T e,i ∼ 0, ∇p ∼ 0 ,…”

Section: Preliminariesmentioning

confidence: 99%

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Quaternionic approach on the Dirac–Maxwell, Bernoulli and Navier–Stokes equations for dyonic fluid plasma

Chanyal

2019

Int. J. Mod. Phys. A

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Applying the Hamilton's quaternion algebra, we propose the generalized electromagnetic-fluid dynamics of dyons governed by the combination of the Dirac-Maxwell, Bernoulli and Navier-Stokes equations. The generalized quaternionic hydro-electromagnetic field of dyonic cold plasma consist the electrons and the magnetic monopoles in which there exist dual-mass and dual-charge species in presence of dyons. We construct the conservation of energy and conservation of momentum equations by equating the quaternionic scalar and vector parts for generalized hydro-electromagnetic field of dyonic cold plasma. We propose the quaternionic form of conservation of energy is related to the Bernoulli's like equation while the conservation of momentum is related to Navier-Stokes like equation for dynamics of dyonic plasma fluid. Further, the continuity equation i.e. the conservation of electric and magnetic charges with the dynamics of hydro-electric and hydro-magnetic flow of conducting cold plasma fluid is also analyzed. The quaternionic formalism for dyonic plasma wave emphasizes that there are two types of waves propagation namely the Langmuir like wave propagation due to electrons, and the 't Hooft-Polyakov like wave propagation due to magnetic monopoles.

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Section: Preliminariesmentioning

confidence: 99%

“…where we neglect the dyonic pressure gradient term (∇p) D to considering cold plasma approximation [17]. The above equations ( 42)-( 47) are well known equations for dual field of massive dyons.…”

Section: Generalized Dual Mhd Of Cold Plasma In Hamilton Spacementioning

confidence: 99%

Quaternionic approach on the Dirac–Maxwell, Bernoulli and Navier–Stokes equations for dyonic fluid plasma

Chanyal

2019

Int. J. Mod. Phys. A

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“…Chanyal [18][19] proposed the quaternionic covariant theory of four-dimensional particle dyons in the form of relativistic quantum mechanics and also focused on the quantized Dirac-Maxwell equations for dyons. Recently, in magneto-hydrodynamics, the quaternionic dual fields equations for dyonic cold plasma have been analyzed [20]. Further, it has been developed Dirac-Maxwell, Bernoulli, and Navier Stokes like equations for dyonic fluidplasma in the generalized quaternionic field [21].…”

Section: Introductionmentioning

confidence: 99%

On the quaternion transformation and field equations in curved space-time

Chanyal¹

2021

Preprint

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In this paper, we use four-dimensional quaternionic algebra to describing space-time geometry in curvature form. The transformation relations of a quaternionic variable are established with the help of basis transformations of quaternion algebra. We deduced the quaternionic covariant derivative that explains how the quaternion components vary with scalar and vector fields. The quaternionic metric tensor and geodesic equation are also discussed to describing the quaternionic line element in curved space-time. Moreover, we discussed an expression for the Riemannian Christoffel curvature tensor in terms of the quaternionic metric tensor. We have deduced the quaternionic Einstein's field-like equation which shows an equivalence between quaternionic matter and geometry.

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“…Besides, the quaternionic algebra has also been used to describe the rotational motion of a rigid body where the quaternionic unit elements are directly connected with matrices of rotational group SO(3) [7]. Further, the quaternion algebra explained the special theory of relativity [8], Dirac Lagrangian [9], superluminal transformations for tachyons [10], wave equation in curved space-time [11], electromagnetic-field equations [12], gravi-electromagnetism [13], quantum mechanics [14,15], particle in a relativistic box [16] and dual magneto-hydrodynamics of dyonic cold plasma [17]. On the other hand, many authors [18]- [37] have used hyper-complex algebras to study the several theories in different branches of physics.…”

Section: Introductionmentioning

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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Quaternionic Approach to Dual Magnetohydrodynamics of Dyonic Cold Plasma

Cited by 21 publications

References 48 publications

Quaternionic approach on the Dirac–Maxwell, Bernoulli and Navier–Stokes equations for dyonic fluid plasma

Quaternionic approach on the Dirac–Maxwell, Bernoulli and Navier–Stokes equations for dyonic fluid plasma

On the quaternion transformation and field equations in curved space-time

A comparative study of quaternionic rotational Dirac equation and its interpretation

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