Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

Rawat, Ashish; Rawat, Seema; Li, Tianjun; Negi, O. P. S.

doi:10.1007/s10773-012-1206-7

Cited by 7 publications

(3 citation statements)

References 28 publications

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“…have been discussed in view of Minkowski structure. The generalized quaternionic rotational Dirac equation and its solutions for fermions without EM-field has been discussed in equation (29). The generalized QRD equation has the benefit of representing both aspects as rotational energy and rotating momentum corresponding to quaternionic scalar and vector components.…”

Section: Discussionmentioning

confidence: 99%

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Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field

Bhatt,

Chanyal

2022

Preprint

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Starting with the quaternionic Minkowski space-time and its four-vector representation, a rotational analogue of the quaternionic Dirac equation in the electromagnetic field is developed, which includes not only the energy solutions but also the angular momentum solutions for rotating Dirac fermions. The striking feature of the quaternionic approach is that it depicts a unified representation of energy-momentum in a single framework as the space-time. Furthermore, we establish the generalized Schrodinger-Pauli-like equation associated with generalized electric and magnetic dipole energies that corresponding to their dipole moments. As such, the present analysis deals with the invariant behavior of the extended quaternionic rotational Dirac equation under Lorentz-Poincaré, Gauge, duality, and CPT invariance.

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Section: Discussionmentioning

confidence: 99%

“…Even so, the quaternionic basis may also be shown as a 2 × 2 matrix form, such that e 0 = 1 2×2 and e j = −iσ j where σ j are the standard Pauli matrices [29]. Furthermore, quaternions show a remarkable resemblance to rotational tau matrices (or isospin matrices) and can be utilized to discuss particle rotational motion [37].…”

Section: The Quaternionsmentioning

confidence: 99%

Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field

Bhatt,

Chanyal

2022

Preprint

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“…In recent years, quaternions have emerged as powerful tools in higher-dimensional quantum mechanics as they provide homogeneous four-dimensional structures in relativistic quantum mechanics and provide representations in terms of compact notations [1][2][3]. Also, spin is a natural outcome of using quaternion as they are represented in terms of Pauli spin matrices [4,5] so their use becomes necessary while dealing with nonzero spin particles.…”

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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Supersymmetry breaking in quaternion space

Rawat,

Dabas

et al. 2023

Indian J Phys

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Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

Cited by 7 publications

References 28 publications

Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field

Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field

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

Supersymmetry breaking in quaternion space

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