The Lamb shift in hydrogen spectrum is obtained here in the framework of some weak generalization of the classical Maxwell electrodynamics. It is shown that weakly generalized classical Maxwell electrodynamics can describe the intra-atomic phenomena with the same success as relativistic quantum mechanics can do. Group-theoretical grounds for the description of fermionic states by bosonic system...

In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that weakly generalized classical Maxwell electrodynamics can describe the intraatomic phenomena with the same success as relativistic quantum mechanics can do. Group-theoretical grounds for the description of fermionic states by bosonic s...

In a gravitational field, we analyze the Maxwell equations, the correponding electromagnetic wave and continuity equations. A particular solution for parellel electric and magnetic fields in a gravitational background is presented. These solutions also satisfy the free-wave equations and the phenomenology suggested by plasma physics.

1. SOBOLEV SPACES AND WEAK FORMULATIONS Let Ω be a bounded Lipschitz domain in R. We introduce the Sobolev spaces H(curl ; Ω) = {v ∈ L(Ω), curlv ∈ L(Ω)}, H(div; Ω) = {v ∈ L(Ω),div v ∈ L(Ω)} The vector fields (E,H) belong to H(curl ; Ω) while the flux (D,B) in H(div; Ω). We shall use the unified notation H(d; Ω) with d = grad , curl , or div. Note that H(grad ; Ω) is the familiar H(Ω) space. The...

We apply the method of slowly-varying amplitudes of the electrical and magnetic fields to integro-differential system of nonlinear Maxwell equations. The equations are reduced to system of differential Nonlinear Maxwell amplitude Equations (NME). The electric and magnetic fields are presented as sums of circular and linear components. Thus, NME is written as a set of Nonlinear Dirac Equations (...

In this paper we find a ground state solution for the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. where V is a possibly singular potential and 3 < p < 5.

In this paper we present an exact calculation of the transfer function associated with the nonlinear Fabry-Perot resonator. While our exact result cannot be evaluated in terms of elementary functions, it does permit us to obtain a number of simple approximate expressions of various orders of accuracy. In addition, our derivation yields criteria of validity for the approximate formulae. Our appr...

A set of self-consistent nonlinear gyrokinetic equations is derived for relativistic charged particles in a general nonuniform magnetized plasma. Full electromagnetic-field fluctuations are considered with spatial and temporal scales given by the low-frequency gyrokinetic ordering. Self-consistency is obtained by combining the nonlinear relativistic gyrokinetic Vlasov equation with the low-freq...

We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is proven to be far more appropriate for the modellization of electromagnetic phenomena. The suitability of this approach will soon be evident to the reader, throug...

We explore the possibility of using the Kaluza-Klein geometry of Riemannian Submersions to modify the classical Maxwell Theory. We further argue that the resulting modification of Electromagnetism— cf. equations (3) as well as (4) and (5)—may be interesting in the context of, among other topics, magnetic oscillations in metals. 1. The Maxwell equations are geometric and can be expressed as equa...