arXiv subjects

B. C. Chanyal

Publications and source records attributed to B. C. Chanyal.

15 recordsLinked to original sources

arXiv2025

Exploring quaternion framework for subluminal to superluminal space transformations in particle dynamics

The present study explores the behavior of quaternionic four-space algebra for subluminal and superluminal spaces. We formulate the generalized Lorentz transformations for quaternionic subluminal, superluminal, and their combined Minkowski spaces. Furthermore, we have studied the relativistic phenomenon of quaternionic length contraction, time dilation, velocity addition, and the Doppler effect for the combination of subluminal and superluminal space. We claim that the transformation between two superluminal spaces is ultimately a subluminal space; the tachyonic behavior reveals itself in the consequences when the two frames are in different spaces (i.e., generalized subluminal-superluminal spaces).

physics.gen-ph↗

arXiv2024

On the existence of quaternion-handedness for the spinor solutions of the Dirac and Majorana neutrinos

This study explores the application of quaternionic left and right-handed algebraic frameworks to discuss the neutrino-handedness behavior. The generalized left and right-handed Dirac equations are expressed in terms of quaternionic four-dimensional non-commutative algebra, which yields helicity eigenspinors with definite spin states for Dirac neutrino eigenstates. We establish the spinor states of energy and momentum solutions for Dirac neutrinos and antineutrinos revealed by the non-commutative nature of quaternionic algebra. Furthermore, we expand the quaternionic Dirac spinor solutions to Majorana-like spinor solutions, which represent the mass eigenstates for Majorana neutrinos. By examining two-flavor neutrino oscillation, we express the quaternionic energy and momentum eigenstates of Dirac and Majorana neutrinos, as well as their oscillation probabilities. The estimated quaternionic-based probability supports neutrinos' massive nature and the presence of their right chiral components. The current quaternionic theory has the benefit of identifying the distinct properties of left and right-handed neutrinos, as well as anti-neutrinos, within a unified framework.

physics.gen-ph↗

arXiv2024

Z_2 Graded Lie Algebra of Quaternions and Superconformal Algebra in D=4 dimensions

In the present discussion, we have studied the Z2-grading of quaternion algebra (H). We have made an attempt to extend the quaternion Lie algebra to the graded Lie algebra by using the matrix representations of quaternion units. The generalized Jacobi identities of Z2-graded algebra then result in symmetric graded partners (N1;N2;N3). The graded partner algebra (F) of quaternions (H) thus has been constructed from this complete set of graded partner units (N1;N2;N3), and N0 = C. Keeping in view the algebraic properties of the graded partner algebra (F), the Z2-graded superspace (Sl;m) of quaternion algebra (H) has been constructed. It has been shown that the antiunitary quaternionic supergroup UUa(l;m;H) describes the isometries of Z2-graded superspace (Sl;m). The Superconformal algebra in D = 4 dimensions is then established, where the bosonic sector of the Superconformal algebra has been constructed from the quaternion algebra (H) and the fermionic sector from the graded partner algebra (F).

physics.gen-ph↗

arXiv2023

A possibility of Klein Paradox in quaternionic (3+1) frame

In light of the significance of non-commutative quaternionic algebra in modern physics, the current study proposes the existence of the Klein paradox in the quaternionic (3+1)-dimensional space-time structure. By introducing the quaternionic wave function, we rewrite the Klein-Gordon equation in an extended quaternionic form that includes scalar and vector fields. Because quaternionic fields are non-commutative, the quaternionic Klein-Gordon equation provides three separate sets of the probability density and probability current density of relativistic particles. We explore the significance of these probability densities by determining the reflection and transmission coefficients for the quaternionic relativistic step potential. Furthermore, we also discuss the quaternionic version of the oscillatory, tunnelling, and Klein zones for the quaternionic step potential. The Klein paradox occurs only in the Klein zone when the impacted particle's kinetic energy is less than \mathbb{V}_{0}-m_{0}c^{2}. Therefore, it is emphasized that for the quaternionic Klein paradox, the quaternionic reflection coefficient becomes exclusively higher than value one while the quaternionic transmission coefficient becomes lower than zero.

physics.gen-ph↗

arXiv2022

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

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, gauge, duality, and CPT invariance.

physics.gen-ph↗

arXiv2021

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

In this paper, we use four-dimensional quaternionic algebra to describing space-time field equations 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 form of Einstein-field-like equation which shows an equivalence between quaternionic matter and geometry.

physics.gen-ph↗

arXiv2019

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

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.

physics.gen-ph↗

arXiv2019

A comparative study of quaternionic rotational Dirac equation and its interpretation

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 four-component 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.

physics.gen-ph↗

arXiv2018

Quaternionic approach to dual Magneto-hydrodynamics of dyonic cold plasma

The dual magneto-hydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual fields equations, namely, the hydro-electric and hydro-magnetic fields equations which are an analogous to the generalized Lamb vector field and vorticity field equations of dyonic cold plasma fluid. Further, we derive the quaternionic Dirac-Maxwell equations for dual magneto-hydrodynamics of dyonic cold plasma. We also obtain the quaternionic dual continuity equations that describe the transport of dyonic fluid. Finally, we establish an analogy of Alfven wave equation which may generate from the flow of magnetic monopoles in the dyonic field of cold plasma. The present quaternionic formulation for dyonic cold plasma is well invariant under the duality, Lorentz and CPT transformations.

physics.gen-ph↗

arXiv2018

A new development in quantum field equations of dyons

In this study, we describe a novel approach to quantum phenomena of the generalized electromagnetic fields of dyons with quaternionic analysis. Starting with quaternionic quantum wave equations, we have established a quantized condition for time coordinate that transforms microscopic to macroscopic fields. In view of classical electromagnetic field equation, we propose a new set of quantized Proca-Maxwell's equations for dyons. Furthermore, a quantized form of four-currents densities and the quantized Lorentz gauge conditions, respectively for electric and magnetic potentials of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons which associated with a torque density result from the two spin states. The quantized Klein-Gordon like field equations and the unified quaternionic electromagnetic potential wave equations for massive dyons are demonstrated. Moreover, we investigate the quaternionic quantized relativistic Dirac field equations for massive dyons, which indicated that there will be the existence of antiparticle of dyons called antidyons.

physics.gen-ph↗

arXiv2017

A relativistic quantum theory of dyons wave propagation

Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the electric and magnetic charge of dyons. We also demonstrate the universal quantum wave equations for two four-potentials as well as two four-currents of dyons. The generalized continuity equations for massive dyons in case of quantum fields are expressed. Furthermore, we concluded that the quantum generalization of electromagnetic field equations of dyons can be related to analogous London field equations (i.e., current to electromagnetic fields in and around a superconductor).

quant-ph↗

arXiv2014

Octonionic Gravi-electromagnetism and Dark Matter

An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic unified gauge formulation for SU(2) ?X U(1) electroweak theory and SU(3) X? SU(2) ?X U(1) grand unified theory. De- scribing the octonion eight dimensional space as the combination of two quaternionic spaces (namely associated with the electromagnetic interaction (EM-space) and linear gravitational interaction (G-space)), we have reexamined the unified picture of EM-G space in terms of oc- tonionic split formulation in consistent manner. Consequently, we have obtained the various field equations for unified gravi-electromagnetic interactions. Furthermore, we have recon- structed the field equations of hot and cold dark matter in terms of split octonions. It is shown that the difference between the octonion cold dark matter (OCDM) and the octonion hot dark matter (OHDM) is significant in the formulating of structure of these two, because the velocities of octonion hot dark matter cause it to wipe out structure on small scales.

physics.gen-ph↗

arXiv2012

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann λmatrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann λmatrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons.

physics.gen-ph↗

arXiv2010

Generalized Split-Octonion Electrodynamics

Starting with the usual definitions of octonions and split octonions in terms of Zorn vector matrix realization, we have made an attempt to write the consistent form of generalized Maxwell's equations in presence of electric and magnetic charges (dyons). We have thus written the generalized potential, generalized field, and generalized current of dyons in terms of split octonions and accordingly the split octonion forms of generalized Dirac Maxwell's equations are obtained in compact and consistent manner. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.

physics.gen-ph↗

arXiv2009

Generalized Octonion Electrodynamics

We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion electrodynamics in manifestly covariant and consistent manner.

physics.gen-ph↗