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We show that the linearized equations of the incompressible elastic medium admit a `Maxwell form in which the shear component of the stress vector plays the role of the electric field, and the vorticity plays the role of the magnetic field. Conversely, the set of dynamic Maxwell equations are strict mathematical corollaries from the governing equations of the incompressible elastic medium. This suggests that the nature of `electromagnetic field may actually be related to an elastic continuous medium. The analogy is complete if the medium is assumed to behave as fluid in shear motions, while it may still behave as elastic solid under compressional motions. Then the governing equations of the elastic fluid are re-derived in the Eulerian frame by replacing the partial time derivatives by the properly invariant (frame indifferent) time rates. The `Maxwell from of the frame indifferent formulation gives the frame indifferent system that is to replace the Maxwell system. This new system comprises terms already present in the classical Maxwell equations, alongside terms that are the progenitors of the Biot--Savart, Oersted--Amperes, and Lorentz--force laws. Thus a frame indifferent (truly covariant) formulation of electromagnetism is achieved from a single postulate that the electromagnetic field is a kind of elastic (partly liquid partly solid) continuum.
The dynamics of any classical-mechanics system can be formulated in the reparametrization-invariant (RI) form (that is we use the parametric representation for trajectories, ${bf x}={bf x}(tau)$, $t=t(tau)$ instead of ${bf x}={bf x}(t)$). In this ped
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Greens functions in the frequency domain for the Maxwells equations and the elastic wave equation in layered media. The formulation can be used to decompose the Maxwells Greens fu
A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eige
The contraction of the Poincare group with respect to the space trans- lations subgroup gives rise to a group that bears a certain duality relation to the Galilei group, that is, the contraction limit of the Poincare group with respect to the time tr
Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charg