Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons

Bisht, P. S.; Negi, O. P. S.

doi:10.1007/s10773-007-9591-z

Cited by 4 publications

(10 citation statements)

References 66 publications

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“…An octonion x is expressed [48][49][50][51][52][53][54] as a set of eight real numbers Here the octonion algebra O is described over the algebra of rational numbers having the vector space of dimension 8. Octonion algebra is non associative.…”

Section: Octonion Definitionmentioning

confidence: 99%

“…In recent years, it has also drawn interests of many [38][39][40][41][42][43][44][45][46][47] towards the developments of wave equation and octonion form of Maxwell's equations. We [48][49][50][51][52][53][54] have also studied octonion electrodynamics, dyonic field equation and octonion gauge analyticity of dyons consistently and obtained the corresponding field equations (Maxwell's equations) and equation of motion in compact and simpler formulation. Keeping in view the recent interests on the existence of monopoles and dyons at one end and quaternion-octonion formulation of generalized Dirac-Maxwell's (GDM) equations at other end, we [55] have reformulated the generalized Dirac-Maxwell's equations of dyons by means of octonion variables in compact and consistent manner.…”

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confidence: 99%

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Generalized Split-Octonion Electrodynamics

2011

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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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Section: Octonion Definitionmentioning

confidence: 99%

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confidence: 99%

Generalized Split-Octonion Electrodynamics

2011

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“…Let us define [6][7][8][47][48][49][50] the generalized electric ( − → E ) and magnetic ( − → H ) fields of dyons in terms of components of electric and magnetic four potentials as…”

Section: Octonion Formulation For Generalized Fields Of Dyonsmentioning

confidence: 99%

“…where − → = − → H + ie 7 − → E is the generalized vector field [6][7][8][47][48][49][50] of dyons. Now applying the differential operator (22) to (30), we get…”

Section: Octonion Formulation For Generalized Fields Of Dyonsmentioning

confidence: 99%

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Generalized Octonion Electrodynamics

2010

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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

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Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

Rawat

et al. 2012

Int J Theor Phys

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The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and component Dirac Spinors of generalized quaternion Dirac equation of dyons for various energy and spin values are obtained for different cases in order to understand the duality invariance between the electric and magnetic constituents of dyons.

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Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons

Cited by 4 publications

References 66 publications

Generalized Split-Octonion Electrodynamics

Generalized Split-Octonion Electrodynamics

Generalized Octonion Electrodynamics

Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

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