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FIZIKA B 17 (2008) 3, 405 - 428
 
INTERPRETATIONS OF OCTONION WAVE EQUATIONS
P. S. BISHTa, B. PANDEYa and O. P. S. NEGIb,
aDepartment of Physics, Kumaun University, S. S. J. Campus, Almora - 263601 (Uttarakhand), India
bInstitute of Theoretical Physics, Chinese Academy of Sciences,
KITP Building Room No.- 6304, Hai Dian Qu Zhong Guan Chun Dong Lu, 55 Hao, Beijing - 100080, P. R. China
E-mail addresses: ps_bisht123@rediffmail.com,
ops_negi@yahoo.co.in
Received 13 August 2007; Revised manuscript received 12 August 2008
Accepted 17 September 2008 Online 30 October 2008
The interpretations of octonion wave equations in eight-dimensional
space-time is studied. We made an attempt to consider 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. It
has been concluded that the component of octonion potential wave equations
behaves neither as the generalized electromagnetic fields of monopoles nor of
the dyons. Rather, it has a 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 R4-space as well as that for
tachyons in T4- space in the absence of other.
PACS numbers: 02.30.-f, 03.65.Fd
UDC 530.145
Keywords: octonion wave equation, eight-dimensional space-time, dyons,
Zorn's vector matrix, bradyons, tachyons
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