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Proca-Maxwell Equations for Dyons with Quaternion

机译:带四元数的二元对的Proca-Maxwell方程

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The quaternions are first hyper-complex numbers, having four-dimensional structure, which may be useful to express the 4-dimensional theory of dyons carrying both electric and magnetic charges. Keeping in mind t’Hooft’s monopole solutions and the fact that despite the potential importance of massive monopole, we discuss a connection between quaternionic complex field, to the generalized electromagnetic field equations of massive dyons. Starting with the Euclidean space-time structure and two four-components theory of dyons, we represent the generalized charge, potential, field and current source in quaternion form with real and imaginary part of electric and magnetic constituents of dyons. We have established the quaternionic formulation of generalized complex-electromagnetic fields equations, generalized Proca-Maxwell’s (GPM) equations and potential wave equations for massive dyons. Thus, the quaternion formulation be adopted in a better way to understand the explanation of complex-field equations as the candidate for the existence of massive monopoles and dyons where the complex parameters be described as the constituents of quaternion.
机译:四元数是第一超复数,具有四维结构,这对于表达同时带有电荷和磁电荷的双子的4维理论可能很有用。请记住t'Hooft的单极子解和尽管有巨大单极子的潜在重要性的事实,但我们讨论了四元离子复数场与广义二极子的广义电磁场方程之间的联系。从欧几里德的时空结构和两个四元组理论开始,我们以四元数形式表示了广义的电荷,电势,场和电流源,并以二元组的电,磁组成部分的实部和虚部表示。我们已经建立了广义复电磁场方程,广义Proca-Maxwell(GPM)方程和大二极体势波方程的四元数公式。因此,以更好的方式采用四元数公式来理解复杂场方程的解释,作为存在大量单极子和二元极的候选对象,其中复杂参数被描述为四元数的组成部分。

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