A new approach is proposed for an electromagnetic field geometrisation. We show that interacting Maxwell and Dirac fields can be considered as a single connected space-time 4-manifold. The Dirac spinors appear wihtin such approach as basic fanctions for the manifold fundamental group representation and electric and magnertic fields appear as components of a curvature tensor of the manifold covering space.
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal symmetries within one symmetry group. We suppose that nonelectromagnetic interactions appear within such approach as the deviations of the metrics from the euclidian form. The expression for the long-range part of "effective" nucleon-nucleon potential is derived using this assumption.
We develop a covariant density matrix approach to kinetic theory of QED plasmas subjected into a strong external electromagnetic field. A canonical quantization of the system on space-like hyperplanes in Minkowski space and a covariant generalization of the Coulomb gauge is used. The condensate mode associated with the mean electromagnetic field is separated from the photon degrees of freedom by a time-dependent unitary transformation of both, the dynamical variables and the nonequilibrium statistical operator. Therefore even in the case of strong external fields a perturbative expansion in or…
In the Relativistic Quantum Geometry (RQG) formalism recently introduced, was explored the possibility that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field $θ$, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. In this framework we study jointly the dynamics of electromagnetic fields produced by quantum complex vector fields, which describes charges without …
A manifestly covariant treatment of the free quantum eletromagnetic field, in a linear covariant gauge, is implemented employing the Schwinger's Variational Principle and the B-field formalism. It is also discussed the abelian Proca's model as an example of a system without constraints.
Schwinger pair production in some of space-dependent electromagnetic fields is studied analytically by using worldline instantons formalism for scalar quantum electrodynamics. With the increase of the modified Keldysh parameter $γ_{keb}$, the pair production rate decreases, the region of instanton paths expands regardless of the electromagnetic field form. We also find that all of the paths of the instantons for various electromagnetic fields are exactly in the same plane while with the different elliptical shapes. Moreover, the magnitudes of the normalized instantons action with different ext…
The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Ref. \cite{zz} and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature or acceleration are also investigated.
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and geometrization of material field within the unique topological idea. According to the suggested topological interpretation, the Dirac equations for a free particle and for a hydrogen atom prove to be the group--theoretical relations that account for the symmetry properties of localized microscopic deviations of the space--time geometry from the pseudoeuclidean one (close…
We develop a general formalism to describe the propagation of a near-resonant electromagnetic field in a medium composed of magnetodielectric resonators. As the size and the spatial separation of nanofabricated resonators in a metamaterial array is frequently less than the wavelength, we describe them as discrete scatterers, supporting a single mode of current oscillation represented by a single dynamic variable. We derive a Lagrangian and Hamiltonian formalism for the coupled electromagnetic fields and oscillating currents in the length gauge, obtained by the Power-Zienau-Woolley transformati…
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of $\BQ=4.4\times10^9$~T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polar…
Modified Langevin noise formalism for multiple quantum emitters in dispersive electromagnetic environments out of equilibrium
Scuola Superiore Meridionale（南方高等学院）；Department of Electrical Engineering and Information Technology, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学电气与信息工程学院）
Radiative energy and momentum transfer due to fluctuations of electromagnetic fields arising due to temperature difference between objects is described in terms of the cross-spectral densities of the electromagnetic fields. We derive relations between thermal non-equilibrium contributions to energy and momentum transfer and surface integrals of tangential components of the dyadic Green's functions of the vector Helmholtz equation. The expressions derived here are applicable to objects of arbitrary shapes, dielectric functions, as well as magnetic permeabilities. For the case of radiative trans…
The Green-function formalism for the electromagnetic field in a magnetoelectric (ME) medium is constructed, as a generalization of conventional Casimir theory. Zero temperature is assumed. It is shown how the formalism predicts electromagnetic momentum to be extracted from the vacuum field, just analogous to how energy is extracted in the Casimir case. The possibility of extracting momentum from vacuum was discussed recently by Feigel [Phys. Rev. Lett. 92, 020404 (2004)]. By contrast to Feigel's approach, we assume that the ME coupling occurs naturally, and is not produced by external strong f…
In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the Canonical Commutation Relations. The corresponding paradigm is a space-time filled with two-dimensional quantum harmonic oscillators. Mathematically, this is equivalent with two additional dimensions penetrated by the electromagnetic waves.
Numerical Framework for Multimode Jaynes- and Tavis-Cummings Models Incorporating the Modified Langevin Noise Formalism: Non-Markovian Analysis of Atom-Field Interactions in Dissipative Electromagnetic Environments
We develop a general formalism to describe the interactions between a discrete set of plasmonic resonators mediated by the electromagnetic field. The resulting system of equations for closely-spaced meta-atoms represents a cooperative metamaterial response and we find that collective interactions between asymmetric split-ring resonators arranged in a 2D lattice explains the recent experimental observations of system-size dependent narrowing of the transmission resonance linewidth. We further show that this cooperative narrowing depends sensitively on the lattice spacing.
In this work we present a mathematical description of how one can produce and read a thin hologram. We use different kinds of waves, such as scalar, vector (electromagnetic field, Maxwell-Proca fields, acoustic waves, etc.). For reading of the hologram, we use the Green's function formalism. With the help of computer simulations, we investigate the aberrations created by this procedure for the simplest case: 2d-scalar wave case.
