Quaternionic Integral Representations for Electromagnetic Fields in Chiral Media

Quaternionic Equation for Electromagnetic Fields in Inhomogeneous Media

“…The quaternionic approach to Maxwell's equations for homogeneous media was intensively used in a number of works (e.g., [8], [9], [10], [13]), but even the question as to how to write the Maxwell equations for arbitrary inhomogeneous media in a compact quaternionic form remained open until recently (an attempt in this direction can be found in [5,Section 4.5]). In [12] such a reformulation was proposed in the case of a time-harmonic electromagnetic field and in [11] for the time-dependent case.…”

Quaternionic Fundamental Solutions for Electromagnetic Scattering Problems and Application

“…We denote by H s+1/2 loc (Ω − ) the union of all such H s+1/2 (Ω − R ) . The same will be valid if in (18) we assume the functions u and U to be H(C)valued and each Cartesian component of U satisfy (10) or which is equivalent the whole function U satisfy (12). The operator transforming u into U we denote by Λ , and as we have just seen Λ acts from H s (Γ) to H…”

Octonion Electrodynamics in Isotropic and Chiral Medium

“…In order to write the various quantum equations of dyons in isotropic medium, we start with the definition of homogeneous (isotropic) medium [10][11][12][13] in the generalized electromagnetic fields as,…”

“…[7,8] constructed a self-consistent co-variant theory of generalized electromagnetic fields associated with dyons each carrying the generalized charge as complex quantity with its real and imaginary part as electric and magnetic constituents. Kravchenko and co-authers [9,10] discussed the Maxwell's equations in homogeneous media and accordingly developed [11] the quaternionic reformulation of the time-dependent Maxwell's equations along with the classical solution of a moving source i.e. electron.…”