Octonionic Extension of \(U(1) \times SU(2)\) Gauge Analyticity of Dyons

Abstract

Starting with the generalized electromagnetic (and gravi-magnetic) fields of dyons (and grvito-dyons), the octonion generalization of \(U(1)\times SU(2)\) gauge theories of dyons (and grvito-dyons) has been developed in a consistent way. The resemblance between octonion covariant derivative and the gauge covariant derivative has also been established . Expressing the generalized four - potential, current and fields of dyons (and gravito - dyons) in terms of split octonion variables, we have discussed the consistent forms of \(U(1)\) abelian and \(SU(2)\) non - Abelian gauge theories for dyons (and gravito - dyons). It is shown that the present formalism reproduces the theory of electric (gravitational) charge (mass) in the absence of magnetic (Heavisidean) charge (mass) on dyons (gravito - dyons) or vice versa.