B C Chanyal | GBPUAT (original) (raw)
Books by B C Chanyal
Papers by B C Chanyal
Chinese Journal of Physics, Sep 30, 2024
The European Physical Journal Plus
The European physical journal plus, Mar 3, 2024
International Journal of Geometric Methods in Modern Physics, Dec 7, 2023
arXiv (Cornell University), Jul 18, 2023
In light of the significance of non-commutative quaternionic algebra in modern physics, the curre... more 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 quaternionic wave-function, we rewrite the Klein-Gordon equation in extended quaternionic form that includes scalar and the 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 V0 − m0c 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.
Modern Physics Letters A, Dec 7, 2021
The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confi... more The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3)[Formula: see text] group generators, as well as color quarks representation. We demonstrated the glueballs construction in the extended octonionic color field and also proposed the prerequisite for octonion color confinement of hadrons.
viXra, Oct 1, 2016
The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be ... more The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be useful to express the 4-dimensional theory of dyons carrying both electric and magnetic charges. Keeping in mind t'Hooft's monopole solutions and the fact that despite the potential importance of massive monopole, we discuss a connection between quaternionic complex field, to the generalized electromagnetic field equations of massive dyons. Starting with the Euclidean space-time structure and two four-components theory of dyons, we represent the generalized charge, potential, field and current source in quaternion form with real and imaginary part of electric and magnetic constituents of dyons. We have established the quaternionic formulation of generalized complexelectromagnetic fields equations, generalized Proca-Maxwell's (GPM) equations and potential wave equations for massive dyons. Thus, the quaternion formulation be adopted in a better way to understand the explanation of complex-field equations as the candidate for the existence of massive monopoles and dyons where the complex parameters be described as the constituents of quaternion.
The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be ... more The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be useful to express the 4-dimensional theory of dyons carrying both electric and magnetic charges. Keeping in mind t’Hooft’s monopole solutions and the fact that despite the potential importance of massive monopole, we discuss a connection between quaternionic complex field, to the generalized electromagnetic field equations of massive dyons. Starting with the Euclidean space-time structure and two four-components theory of dyons, we represent the generalized charge, potential, field and current source in quaternion form with real and imaginary part of electric and magnetic constituents of dyons. We have established the quaternionic formulation of generalized complex-electromagnetic fields equations, generalized Proca-Maxwell’s (GPM) equations and potential wave equations for massive dyons. Thus, the quaternion formulation be adopted in a better way to understand the explanation of complex...
International Journal of Geometric Methods in Modern Physics
Starting with the quaternionic Minkowski space–time and its four-vector representation, a rotatio... more 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 corresponds 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.
Modern Physics Letters A, 2021
The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confi... more The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3)[Formula: see text] group generators, as well as color quarks representation. We demonstrated the glueballs construction in the extended octonionic color field and also proposed the prerequisite for octonion color confinement of hadrons.
We have made an attempt to reformulate the generalized field equation of dyons in terms of octoni... more 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.
In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-hal... more In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic division algebra. The generalized quaternionic Dirac equation consist the rotational energy and angular momentum of particle and anti-particle. Accordingly, we also discuss the quaternionic relativistic mass, moment of inertia and rotational energy-momentum four vector 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 spinor forms of quaternionic wave function. We also demonstrate the solutions of quaternionic plane wave equation which analysis the rotational frequency and wave propagation vector of Dirac particles an...
In this paper, we use four-dimensional quaternionic algebra to describing space-time geometry in ... more 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.
viXra, 2016
The vast majority of the dark matter in the universe is believed to be nonbaryonic, which means t... more The vast majority of the dark matter in the universe is believed to be nonbaryonic, which means that it contains no atoms and does not interact with ordinary matter via electromagnetic forces. The nonbaryonic dark matter includes neutrinos, and possibly hypothetical entities such as axions, or supersymmetric particles. Unlike baryonic dark matter, nonbaryonic dark matter does not contribute to the formation of the elements in the early universe (big bang nucleosynthesis) and so its presence is revealed only via its gravitational attraction. The nonbaryonic dark matter is evident through its gravitational effect only. There are two type of nonbaryonic dark matter respectively defined as hot dark matter and cold dark matter. For the existence of nonbaryonic dark matter in this universe we can used the higher dimensional division algebra. There exists four normed division algebras: the real numbers, complex numbers, quaternions, and octonions. Since, the octonions are the last division...
viXra, 2013
In this paper, we have made an attempt to discuss the role of octonions in gravity and dark matte... more In this paper, we have made an attempt to discuss the role of octonions in gravity and dark matter where, we have described the octonion space as the combination of two quaternionic spaces namely gravitational G-space and electromagnetic EM-space. It is shown that octonionic hot dark matter contains the photon and graviton (i.e. massless particles) while the octonionic cold dark matter is associated with the W±, Z (massive) bosons.
viXra, 2013
Starting with the usual definations of octonions and split octonions in terms of Zorn vector matr... more Starting with the usual definations 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. We have thus written the generalized split octonion potential wave equations and the generalized fields equation of dyons in split octonions. Accordingly the split octonion forms of generalized Dirac Maxwell’s equations are obtained in compact and consistent manner. Accordingly, we have made an attempt to investigate the work energy theorem or “Poynting Theorem”, Maxwell stress tensor and Lorentz invariant for generalized fields of dyons in split octonion electrodynamics. Our theory of dyons in split octonion formulations is discussed in term of simple and compact notations. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.
Canadian Journal of Physics, 2018
In this study, we describe a novel approach to quantum phenomena of the generalized electromagnet... more 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 the classical electromagnetic field equations, we propose a new set of quantized Proca–Maxwell’s equations for dyons. Furthermore, a quantized form of four-current densities and the quantized Lorentz gauge conditions for electric and magnetic potentials, respectively, of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons, which are 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...
Hepatology, 2018
Single crystal of yttrium aluminum borate YAl 3 (BO 3) 4 doped with chromium ions (1 at.%) was st... more Single crystal of yttrium aluminum borate YAl 3 (BO 3) 4 doped with chromium ions (1 at.%) was studied using electron paramagnetic resonance spectroscopy. It is shown that chromium ions introduced into the sample occupy yttrium ion sites in the crystal structure. The parameters of the spin Hamiltonian of Cr 3+ ions in the YAl 3 (BO 3) 4 matrix are determined at different temperatures. The sign of the fine structure parameter D allows the conclusion that the chromium ions in YAl 3 (BO 3) 4 single crystals have an easy-plane anisotropy.
Chinese Journal of Physics, Sep 30, 2024
The European Physical Journal Plus
The European physical journal plus, Mar 3, 2024
International Journal of Geometric Methods in Modern Physics, Dec 7, 2023
arXiv (Cornell University), Jul 18, 2023
In light of the significance of non-commutative quaternionic algebra in modern physics, the curre... more 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 quaternionic wave-function, we rewrite the Klein-Gordon equation in extended quaternionic form that includes scalar and the 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 V0 − m0c 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.
Modern Physics Letters A, Dec 7, 2021
The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confi... more The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3)[Formula: see text] group generators, as well as color quarks representation. We demonstrated the glueballs construction in the extended octonionic color field and also proposed the prerequisite for octonion color confinement of hadrons.
viXra, Oct 1, 2016
The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be ... more The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be useful to express the 4-dimensional theory of dyons carrying both electric and magnetic charges. Keeping in mind t'Hooft's monopole solutions and the fact that despite the potential importance of massive monopole, we discuss a connection between quaternionic complex field, to the generalized electromagnetic field equations of massive dyons. Starting with the Euclidean space-time structure and two four-components theory of dyons, we represent the generalized charge, potential, field and current source in quaternion form with real and imaginary part of electric and magnetic constituents of dyons. We have established the quaternionic formulation of generalized complexelectromagnetic fields equations, generalized Proca-Maxwell's (GPM) equations and potential wave equations for massive dyons. Thus, the quaternion formulation be adopted in a better way to understand the explanation of complex-field equations as the candidate for the existence of massive monopoles and dyons where the complex parameters be described as the constituents of quaternion.
The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be ... more The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be useful to express the 4-dimensional theory of dyons carrying both electric and magnetic charges. Keeping in mind t’Hooft’s monopole solutions and the fact that despite the potential importance of massive monopole, we discuss a connection between quaternionic complex field, to the generalized electromagnetic field equations of massive dyons. Starting with the Euclidean space-time structure and two four-components theory of dyons, we represent the generalized charge, potential, field and current source in quaternion form with real and imaginary part of electric and magnetic constituents of dyons. We have established the quaternionic formulation of generalized complex-electromagnetic fields equations, generalized Proca-Maxwell’s (GPM) equations and potential wave equations for massive dyons. Thus, the quaternion formulation be adopted in a better way to understand the explanation of complex...
International Journal of Geometric Methods in Modern Physics
Starting with the quaternionic Minkowski space–time and its four-vector representation, a rotatio... more 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 corresponds 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.
Modern Physics Letters A, 2021
The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confi... more The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3)[Formula: see text] group generators, as well as color quarks representation. We demonstrated the glueballs construction in the extended octonionic color field and also proposed the prerequisite for octonion color confinement of hadrons.
We have made an attempt to reformulate the generalized field equation of dyons in terms of octoni... more 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.
In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-hal... more In this study, we develop the generalized Dirac like four-momentum equation for rotating spin-half particles in four-dimensional quaternionic division algebra. The generalized quaternionic Dirac equation consist the rotational energy and angular momentum of particle and anti-particle. Accordingly, we also discuss the quaternionic relativistic mass, moment of inertia and rotational energy-momentum four vector 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 spinor forms of quaternionic wave function. We also demonstrate the solutions of quaternionic plane wave equation which analysis the rotational frequency and wave propagation vector of Dirac particles an...
In this paper, we use four-dimensional quaternionic algebra to describing space-time geometry in ... more 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.
viXra, 2016
The vast majority of the dark matter in the universe is believed to be nonbaryonic, which means t... more The vast majority of the dark matter in the universe is believed to be nonbaryonic, which means that it contains no atoms and does not interact with ordinary matter via electromagnetic forces. The nonbaryonic dark matter includes neutrinos, and possibly hypothetical entities such as axions, or supersymmetric particles. Unlike baryonic dark matter, nonbaryonic dark matter does not contribute to the formation of the elements in the early universe (big bang nucleosynthesis) and so its presence is revealed only via its gravitational attraction. The nonbaryonic dark matter is evident through its gravitational effect only. There are two type of nonbaryonic dark matter respectively defined as hot dark matter and cold dark matter. For the existence of nonbaryonic dark matter in this universe we can used the higher dimensional division algebra. There exists four normed division algebras: the real numbers, complex numbers, quaternions, and octonions. Since, the octonions are the last division...
viXra, 2013
In this paper, we have made an attempt to discuss the role of octonions in gravity and dark matte... more In this paper, we have made an attempt to discuss the role of octonions in gravity and dark matter where, we have described the octonion space as the combination of two quaternionic spaces namely gravitational G-space and electromagnetic EM-space. It is shown that octonionic hot dark matter contains the photon and graviton (i.e. massless particles) while the octonionic cold dark matter is associated with the W±, Z (massive) bosons.
viXra, 2013
Starting with the usual definations of octonions and split octonions in terms of Zorn vector matr... more Starting with the usual definations 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. We have thus written the generalized split octonion potential wave equations and the generalized fields equation of dyons in split octonions. Accordingly the split octonion forms of generalized Dirac Maxwell’s equations are obtained in compact and consistent manner. Accordingly, we have made an attempt to investigate the work energy theorem or “Poynting Theorem”, Maxwell stress tensor and Lorentz invariant for generalized fields of dyons in split octonion electrodynamics. Our theory of dyons in split octonion formulations is discussed in term of simple and compact notations. This theory reproduces the dynamic of electric (magnetic) in the absence of magnetic (electric) charges.
Canadian Journal of Physics, 2018
In this study, we describe a novel approach to quantum phenomena of the generalized electromagnet... more 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 the classical electromagnetic field equations, we propose a new set of quantized Proca–Maxwell’s equations for dyons. Furthermore, a quantized form of four-current densities and the quantized Lorentz gauge conditions for electric and magnetic potentials, respectively, of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons, which are 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...
Hepatology, 2018
Single crystal of yttrium aluminum borate YAl 3 (BO 3) 4 doped with chromium ions (1 at.%) was st... more Single crystal of yttrium aluminum borate YAl 3 (BO 3) 4 doped with chromium ions (1 at.%) was studied using electron paramagnetic resonance spectroscopy. It is shown that chromium ions introduced into the sample occupy yttrium ion sites in the crystal structure. The parameters of the spin Hamiltonian of Cr 3+ ions in the YAl 3 (BO 3) 4 matrix are determined at different temperatures. The sign of the fine structure parameter D allows the conclusion that the chromium ions in YAl 3 (BO 3) 4 single crystals have an easy-plane anisotropy.
Ukrainian Journal of Physics, 2017
The evolution of a quantum gravitational system (QGS) with the maximally symmetric geometry in th... more The evolution of a quantum gravitational system (QGS) with the maximally symmetric geometry in the epoch close to the Planck one is investigated. The state vector of the QGS satisfies the set of wave equations which describes the time evolution of the quantum system in the space of quantum fields. It is shown that, for the time arrow from past to future, the state vector describes the QGS contracting for the negative values of the cosmic scale factor and expanding for its positive values. The intensity distributions of matter for two exactly solvable models of spatially closed and flat QGSs formed by dust and radiation are calculated. The analogies with known phenomena in quantum mechanics and optics are drawn. K e y w o r d s: quantum gravity, quantum geometrodynamics, cosmology.