Related papers: Covariant electrodynamics in linear media: Optical…
We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
The similarity between Finsler and Riemann geometry is an intriguing starting point to extend general relativity. The lack of quadratic restriction over the line element (color) naturally generalize the Riemannian case and breaks the local…
There is ongoing interest in adopting various tools and ideas from general relativity for optical applications and the study of light propagation through natural or engineered media. Here, the covariant kinematics of light propagating…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
This paper is intended to investigate the relation between electrodynamics in anisotropic material media and its analogous formulation in an spacetime, with non-null Riemann curvature tensor. After discussing the electromagnetism via chiral…
Recently, Feigel has predicted a new effect in magnetoelectric media. The theoretical evaluation of this effect requires a careful analysis of a dynamics of the moving magnetoelectric medium and, in particular, the derivation of the…
We present a geometrical formulation of nonlinear electrodynamics by expressing its principal symbol as an optical metric-induced object. Under the assumption of no birefringence, we show that the evolution of linear perturbations can be…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
We show that the Einstein covariance principle provides an opportunity to generate infinitely many solutions of given covariant equation from a known one. With use of this statement we derive exact expressions for charge and current…
We continue the development of a manifestly 4-dimensional, completely covariant, approach to transformation optics in linear dielectric materials begun in a previous paper. This approach, which generalizes the Plebanski based approach, is…
The premetric approach to electrodynamics provides a unified description of a wide class of electromagnetic phenomena. In particular, it involves axion, dilaton and skewon modifications of the classical electrodynamics. This formalism…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H^{ab} = (D, H /c) and…
Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants…
A generally covariant four-dimensional representation of Maxwell's electrodynamics in a generic material medium can be achieved straightforwardly in the metric-free formulation of electromagnetism. In this setup, the electromagnetic…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…