Related papers: Application of Herglotz's Variational Principle to…
We consider an elastic-plastic medium whose motion equations are isomorphic to Maxwell's equations. Electrical charges are modeled by pressure centers of the medium. The electric interaction is shown to be concerned with the conservation…
In previous work I have shown that Herglotz actions reproduce the dynamics of classical mechanical theories which exhibit dynamical similarities. Recent work has shown how to extend field theories in both the Lagrangian and de Donder-Weyl…
We develop some ideas about gauge symmetry in the context of Maxwell's theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a…
A fresh approach to the full wave analysis of time evolution of the polarization induced in the electromagnetic scattering from dispersive non magnetic particles is presented. It is grounded on the combination of the Hopfield model for the…
Potential-based formulation with generalized Lorenz gauge can be used in the quantization of electromagnetic fields in inhomogeneous media. However, one often faces the redundancy of modes when finding eigenmodes from potential-based…
We discuss the Lorentz model for dispersion and absorption of radiation in dilute, linear and isotropic materials. Initially, with the purpose of making the paper as self-contained as possible, we reproduce the usual calculations concerning…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
We study interacting electrons in a periodic potential and a uniform magnetic field ${\bf B}$ taking the spin-orbit interaction into account. We first establish a perturbation expansion for those electrons with respect to the Bloch states…
We derive Huygens' principle for electrodynamics in terms of 4-vector potentials defined as distributions supported on a surface surrounding the charge-current density. By combining the Pauli algebra with distribution theory, a compact and…
We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm…
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…
The electron-electron interaction corrections to the transport coefficients are calculated for a two-dimensional disordered metal in a parallel magnetic field via the quantum kinetic equation approach. For the thermal transport, three…
We investigate divergence-type theories (DTT) describing the dissipative interaction between a field and a fluid. We look for theories which, under equilibrium conditions, reduce to the theory of a Klein-Gordon scalar field and a perfect…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
A hydrodynamic-type, macroscopic theory was set up recently to simultaneously account for dissipation and dispersion of electromagnetic field, in nonstationary condensed systems of nonlinear constitutive relations~\cite{JL}. Since it was…
We investigate the relativistic dynamics of a spin half particle in the presence of a Lorentz-violating background within the framework of effective field theory. A modified Dirac Hamiltonian is considered, arising from a CPT odd coupling…
An overarching question in strongly correlated electron systems is how the landscape of quantum phases emerges from electron correlations. The method of extended dynamical mean field theory (EDMFT) has been developed for clean lattice…
In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve some radiation processes. It indicates that the related method…
We outline a rigorous method which can be used to solve the many-body Schroedinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the…