Related papers: Complex Structures in Electrodynamics
We investigate the topological properties of multiple exceptional points in non-Hermitian two-level systems, emphasizing vorticity as a topological invariant arising from complex energy structures. We categorize EP pairs as fundamental…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
Exact equations describing flexoelectric deformation in solids, derived previously within the framework of a continuum media theory, are partial differential equations of the fourth order. They are too complex to be used in the cases…
We show that the partition function of free Maxwell theory on a generic Euclidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one…
The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material…
Two-dimensional pure electrodynamics is mapped into two-dimensional gravity in the first order formalism at classical and quantum levels. Due to the fact that the degrees of freedom of these two theories do not match, we are enforced to…
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
The prolongation structure of a two-by-two problem is formulated very generally in terms of exterior differential forms on a standard representation of Pauli matrices. The differential system is general without making reference to any…
The aim of this work is to proceed with the development of a model of topological electromagnetism in empty space, proposed by one of us some time ago and based on the existence of a topological structure associated with the radiation…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on…
We construct an explicit covariant Majorana formulation of Maxwell electromagnetism which does not make use of vector 4-potential. This allows to write a ``Dirac'' equation for the photon containing all the known properties of it. In…
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength two-form and induction two-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory…
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action…
There exist non-degenerate 3-form $d\omega_I$, $\omega_I(X,Y)=g(IX,Y)$, for each leftinvariant almost Hermitian structure $(g,I)$, where $g$ is Killing-Cartan metric on the $M=S^3\times S^3=SU(2)\times SU(2)$. Known \cite{H1}, that…
The ongoing scientific interest in the properties and structure of electric double layers (EDLs) stems from their pivotal role in (super)capacitive energy storage, energy harvesting, and water treatment technologies. Classical density…
We generalize the formerly proposed relationship between a special complex geometry (originating from the structure of biquaternion algebra) and induced real geometry of (extended) space-time. The primordial dynamics in complex space allows…
A Dirac electron system in solids mimics a relativistic quantum physics that is compatible with Maxwell's equations, by which we anticipate unified electromagnetic responses. We find a large orbital diamagnetism only along the interplane…