422 research outputs found
Revisiting Quaternionic Dual Electrodynamics
Dual electrodynamics and corresponding Maxwell's equations (in the presence
of monopole only) are revisited from dual symmetry and accordingly the
quaternionic reformulation of field equations and equation of motion is
developed in simple, compact and consistent manner.Comment: 15 page
Super Symmetric Partners in T4- space
Constructing the operators connecting the state of energy associated with
super partner Hamiltonians and super partner potentials for a linear harmonic
oscillator has been discussed and it is shown that any super symmetric eigen
state of one of the super partner potentials in T4-space is paired in energy
with a symmetric eigen state of the other partner potential
Magnetohydrodynamics in Presence of Electric and Magnetic charges
Starting with the generalized electromagnetic field equations of dyons, we
have discussed the theory of magnetohydrodynamics (MHD) of plasma for particles
carrying simultaneously the electric and magnetic charges (namely dyons). It is
shown that the resultant system supports the electromagnetic duality of dyons.
Consequently the frequency of dyonic plasma has been obtained and it is
emphasized that there is a different plasma frequency for each species
depending on wave number k. For k to be real, only those generalized
electromagnetic waves are allowed to pass, for which the usual frequency is
greater than the plasma frequency (i.e. \omega>\omega_{p}). It is shown that
the plasma frequency sets the lower cuts for the frequencies of electromagnetic
radiation that can pass through a plasma . Accordingly the ohm's law has been
reestablished to derive the plasma oscillation equation as well as the
magetohydrodynamic wave equation and the energy of dyons in unique and
consistent manner.Comment: PACS NO: 14.80.Hv (Magnetic Monopoles), 52.30.Cv
(Magnetohydrodynamics -including electron magnetohydrodynamics) Keywords:
Magnetohydrodynamics, dyons, electromagnetic fields
Electromagnetic Duality, Quaternion and Supersymmetric Gauge Theories of Dyons
Starting with the generalized potentials, currents, field tensors and
electromagnetic vector fields of dyons as the complex complex quantities with
real and imaginary counter parts as electric and magnetic constituents, we have
established the electromagnetic duality for various fields and equations of
motion associated with dyons in consistent way. It has been shown that the
manifestly covariant forms of generalized field equations and equation of
motion of dyons are invariant under duality transformations. Quaternionic
formulation for generalized fields of dyons are developed and corresponding
field equations are derived in compact and simpler manner. Supersymmetric gauge
theories are accordingly reviewed to discuss the behaviour of dualities
associated with BPS mass formula of dyons in terms of supersymmetric charges.
Consequently, the higher dimensional supersymmetric gauge theories for N=2 and
N=4 supersymmetries are analysed over the fields of complex and quaternions
respectively
Interpretations of Octonion Wave Equations
The interpretations of octonion wave equations in eight dimensional
space-time have been discussed. We have made an attempt to discuss the octonion
field equation as the equation of motion for particles carrying simultaneously
electric and magnetic charges (i.e. dyons) in external and internal spaces
respectively. It has been concluded that the component of octonion potential
wave equations behaves neither the generalized electromagnetic fields of
monopoles nor the dyons. Rather, they have the mixed behaviour of
electromagnetic fields associated with the electric and magnetic charges in
external and internal spaces. We have also made an attempt to investigate the
split octonion wave equation and its interpretation in classical
electrodynamics and accordingly the consistent and compact forms of
eight-dimensional potential and current equation of dyons are obtained in terms
of Zorn's vector matrix realization of split octonions.Visualizing the external
four space as the localization space for tachyons, it is shown that the split
octonion wave equation reduces to the Maxwell's equation (field equation) for
bradyons in R^{4}- space as well as that for tachyons in T^{4}- space in the
absence of other
Octonionic Gauge Formulation for Dyonic Fields
Starting with the generalized field equation of dyons and gravito-dyons, we
study the theory of octonion variables to the SU (2) non-Abelian gauge
formalism. We demonstrate the resemblance of octonion covariant derivative with
the gauge covariant derivative of generalized fields of dyons.Expressing the
generalized four-potential, current and fields of gravito-dyons in terms of
split octonion variables, the U (1) abelian and SU (2) non-Abelian gauge
structure of dyons and gravito-dyons are described. It is emphasized that in
general the generalized four-current is not conserved but only the Noetherian
four-current is considered to be conserved one. The present formalism yields
the theory of electric (gravitational) charge (mass) in the absence of
magnetic(Heavisidean) charge (mass) on dyons (gravito-dyons) or vice versa
Quaternionic Reformulation of Generalized Superluminal Electromagnetic Fields of Dyons
Superluminal electromagnetic fields of dyons are described in T^{4}- space
and Quaternion formulation of various quantum equations is derived. It is shown
that on passing from subluminal to superluminal realm via quaternion the theory
of dyons becomes the Tachyonic dyons. Corresponding field Equations of
Tachyonic dyons are derived in consistent, compact and simpler form.
Abstract Key words- Monopoles, Dyons, Tachyons, Quaternions, Superluminal and
Electromagnetic fields.
Abstract PACS Nos- 03.50 De, 14.80 Hv.Comment: 20 page
Quaternion Generalization of Super Poincare Group
Super Poincare algebra in D = 6 space-time dimensions has been analysed in
terms of quaternion analyticity of Lorentz group. Starting the connection of
quaternion Lorentz group with SO(1; 5) group, the SL(2;H) spinors for Dirac &
Weyl representations of Poincare group are described consistently to extend the
Poincare algebra to Super Poincare algebra for D = 6 space-time.Comment: N
Generalized Electromagnetic fields of Dyons in Inhomogenous Media
Reformulation of the generalized electromagnetic fields of dyons has been
dicussed in inhomogenous media and corresponding quaternionic equations are
derived in compact, simple and unique manner. We have also discussed the
monochromatic fields of generalized electromagnetic fields of dyons in slowly
changing media in a consistent manner
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.Comment: Abstract Key Words: Split octonions, Zorn Vector Matrix Realizations,
Monopoles and dyons; Abstract PACS: 14.80 H
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