University of Khartoum

Derivation of Maxwell-Like Equations from the Quaternionic Dirac's Equation

Derivation of Maxwell-Like Equations from the Quaternionic Dirac's Equation

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dc.contributor.author Arbab, Arbab I.
dc.contributor.other Physics en_US
dc.date 2013-01
dc.date.accessioned 2015-12-13T07:42:30Z
dc.date.available 2015-12-13T07:42:30Z
dc.date.issued 2015-12-13
dc.date.submitted 2015
dc.identifier.uri http://khartoumspace.uofk.edu/handle/123456789/17538
dc.description.abstract Expanding the ordinary Dirac’s equation, 1 c @ @t + ~α · ~∇ψ + imc ¯h ψ = 0, in quaternionic form has yielded Maxwell-like field equations. As in the Maxwell’s formulation, the particle fields are represented by a scalar, ψ0 and a vector ~ψ . The analogy with Maxwell’s equations requires that ψ0 = −cβ ~α · ~ψ , ~ED = c2~α × ~ψ , and ~BD = ~α ψ0 + cβ ~ψ . An alternative solution suggests that monopole-like behaviour accompanies Dirac’s field. In this formulation a field-like representation of Dirac’s particle is derived. It is shown that when the vector field of the particle, ~ψ , is normal to the vector ~α, Dirac’s field represents a medium with maximal conductivity. The energy flux (Poynting vector) of the Dirac’s fields is found to flow in opposite direction to the particle’s motion. An equivalent symmetrised Maxwell’s equations are introduced. A longitudinal (scalar) wave traveling at speed of light is found to accompany magnetic charges flow. This wave is not affected by presence of electric charges and currents. en_US
dc.language.iso en en_US
dc.publisher UOFK en_US
dc.subject Derivation en_US
dc.subject Maxwell en_US
dc.subject equations en_US
dc.subject quaternionic Dirac's equation en_US
dc.title Derivation of Maxwell-Like Equations from the Quaternionic Dirac's Equation en_US
dc.type Publication en_US
dc.Faculty Science en_US

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