A relativistic quantum theory of dyons wave propagation

Chanyal, B. C.

doi:10.1139/cjp-2017-0080

Cited by 25 publications

(8 citation statements)

References 27 publications

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“…We observe that ( 18) is different from the usual expression of generalized Dirac Maxwell equations [12,13,16,19,20], where both of the fields have scalar and vector potentials. In the quaternionic formulation contained in this article, the magnetic field (3) is essentially different from the electric field because of the self-interaction term, and consequently (18) holds in accordance to Maxwell electrodynamics.…”

Section: Quaternionic Electrodynamicsmentioning

confidence: 60%

“…where Q M is the pure quaternionic magnetic charge obtained after integration over the volume of the whole space V. Equations (12)(13) show that the quaternionic magnetic field may admit the existence of magnetic charges for non-singular vector potentials, an important difference to the current formulation of magnetic monopoles, where the vector potential is necessarily singular and the set of singularities comprises the Dirac string.…”

Section: Quaternionic Electrodynamicsmentioning

confidence: 99%

“…Without it, the quantum Lorentz force does not make sense. Compared to the previous quaternionic formulations [8][9][10][11][12][13], the quaternionic formulation of electrodynamics presented in this article is novel because it uses quaternionic vectors, and not quaternionic numbers; more importantly, the theory is novel because of their self-interacting physical character given in (3). The self-interaction component A × A implies that B is not necessarily divergenceless, thus raising the hypothesis of magnetic monopoles solutions within quaternionic quantum mechanics (HQM).…”

mentioning

confidence: 98%

“…There exists an old interest to apply various complex structures to electromagnetism, and we mention applications with complex numbers [6,7], quaternions [8][9][10][11][12][13][14][15], bi-quaternions [16][17][18][19][20][21], hyperbolic quaternions [22], octonions [23][24][25][26], hyperbolic octonions [15,27] and sedenions [28].…”

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confidence: 99%

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Quaternionic electrodynamics

Giardino

2020

Preprint

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Section: Quaternionic Electrodynamicsmentioning

confidence: 60%

Section: Quaternionic Electrodynamicsmentioning

confidence: 99%

mentioning

confidence: 98%

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confidence: 99%

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Quaternionic electrodynamics

Giardino

2020

Preprint

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“…Chanyal [11] and in quantum field theory was used by B.C. Chanyal [12], S.D. Leo [13,14], S. Ulrich [15] and H. Sobhani et al [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Quaternionic quantum mechanics for N = 1, 2, 4 supersymmetry

Rawat

2022

Beni-Suef Univ J Basic Appl Sci

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Background Quaternions have emerged as powerful tools in higher-dimensional quantum mechanics as they provide homogeneous four-dimensional structure in quantum field theories, offer compact representations, and incorporate spin naturally. Quantum field theories then lead to the unification of fundamental interactions so the use of quaternion becomes necessary when we are dealing with higher-dimensional theories. On the other hand, supersymmetry is the theory of bosons and fermions and is an essential constituent of grand unified theories. The use of quaternion in supersymmetric field theories provides an excellent framework for higher-dimensional unification theories. Result A complete theory for supersymmetric quaternionic quantum mechanics has been constructed for N = 1, 2, 4 supersymmetry in terms of one, two, and four supercharges and Hamiltonians, respectively. It has been shown that N = 4 SUSY is the quaternionic extension of the N = 2 complex SUSY and N = 1 real SUSY; also spin is the natural outcome of using quaternion units. Pauli and Dirac Hamiltonian and their relationship have also been obtained in quaternion space. It has been shown that quaternionic quantum mechanics are superior to ordinary and complex quantum mechanics because in the quaternion framework we do not need three different theories for N = 1,2,4 SQM but a single theory only. Conclusions It has been concluded that N = 1 real SUSY is equal to N = 2 complex SUSY which in turn is equal to N = 4 quaternion SUSY so one can arrive at higher-dimensional quantum field theories starting from lower-dimensional quantum theories. Higher-dimensional quaternion field theories are suitable for nonphotonic light cone particles which are not allowed in complex QFT, also noncommutative nature of quaternion gives an extra degree of freedom and may provide the possibility of some new particle, dark matter, or new phenomenon. Though quaternions provide an excellent framework in higher-dimensional field theories, there are certain challenges due to their noncommutativity as calculations become tedious where large terms are involved. Keeping in view the noble features of quaternion, we expect some development to get a better understanding of N = 8 supergravity, maximal supergravity (D = 11 − n), and maximal supersymmetry theories (N = 10) in terms of quaternion operators.

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Utilizing the Caputo fractional derivative for the flux tube close to the neutral points

Durmaz,

Ceyhan,

Özdemir

et al. 2024

Math Methods in App Sciences

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This study examines how fractional derivatives affect the theory of curves and related surfaces, an application area that is expanding daily. There has been limited research on the geometric interpretation of fractional calculus. The present study applied the Caputo fractional calculation method, which has the most suitable structure for geometric computations, to examine the effect of fractional calculus on differential geometry. The Caputo fractional derivative of a constant is zero, enabling the geometric solution and understanding of many fractional physical problems. We examined flux tubes, which are magnetic surfaces that incorporate these lines of magnetic fields as parameter curves. Examples are visualized using mathematical programs for various values of Caputo fractional analysis, employing theory‐related examples. Fractional derivatives and integrals are widely utilized in various disciplines, including mathematics, physics, engineering, biology, and fluid dynamics, as they yield more numerical results than classical solutions. Also, many problems outside the scope of classical analysis methods can be solved using the Caputo fractional calculation approach. In this context, applying the Caputo fractional analytic calculation method in differential geometry yields physically and mathematically relevant findings, particularly in the theory of curves and surfaces.

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A relativistic quantum theory of dyons wave propagation

Cited by 25 publications

References 27 publications

Quaternionic electrodynamics

Quaternionic electrodynamics

Quaternionic quantum mechanics for N = 1, 2, 4 supersymmetry

Utilizing the Caputo fractional derivative for the flux tube close to the neutral points

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