A Study of quaternionic quantized Proca-Maxwell equations
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Date
2022-09
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G.B. Pant University of Agriculture and Technology, Pantnagar, District Udham Singh Nagar, Uttarakhand. PIN - 263145
Abstract
Under this work, we develop the quantum formulation of Proca-Maxwell equations of dyon using quaternionic algebra. The quaternionic algebra is regarded as the four dimensional norm division algebra called as hypercomplex algebra which contains real and imaginary part. The four potential, four current and four fields of dyons are expressed in quaternionic form. We establish an expression for the quaternionic quantized electromagnetic fields of dyon. The quantum Lorenz gauge condition is obtained for the generalized electromagnetic fields of dyon. An approximate relation is expressed for the classical electromagnetic field vector from the quantum electromagnetic field vector. We deduce a set of quaternionic quantized Proca-Maxwell
equations for dyon. We express the quaternionic quantized wave equation for dyon which represents an analogous of Klein-Gordon equation. We discuss the quaternionic form of quantized electromagnetic wave equations and the quantum continuity equation for dyon. We have checked the duality invariance for the quantized Proca-Maxwell equations and wave equation for dyon. Hence, it has shown that the quaternionic quantized Proca-Maxwell equations and wave equations are duality invariant. We also discuss the quaternionic formulation of quantized electromagnetic energy for dyon. As such, the Poynting theorem for the field equations of dyon has been developed. As a result, we have concluded that the quaternionic formalism is a simple, compact and preferable way to represent the quantum analogue of generalized electromagnetic field, Proca-Maxwell equations and wave equations of dyon.