Related papers: Wavelet Electrodynamics I
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
In a gravitational field, we analyze the Maxwell equations, the correponding electromagnetic wave and continuity equations. A particular solution for parellel electric and magnetic fields in a gravitational background is presented. These…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
We investigate wavelet-like localized solutions in nonlinear waveguides, enabled by complementary propagation constants embedded in domains of anomalous dispersion. They are carrier-envelope-phase stable and independent of fine details of…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
A photon-like wavepacket based on novel solutions of Maxwell's equations is proposed. It is believed to be the first 'classical' model that contains so many of the accepted quantum features. In this new work, novel solutions to Maxwell's…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
Highly localized explicit solutions to multidimensional wave and Klein--Gordon--Fock equations are presented. Their Fourier transform is also found explicitly. Solutions depend on a set of parameters, and demonstrate astigmatic properties.…
Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock - Ivanenko. In…
We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some…
We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic…
It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these…
A planar superfluid is considered and interpreted in terms of electromagnetism and gravity. It has previously been suggested that the superfluid flow can be regarded as analogous to an electromagnetic field and that a non-vanishing density…
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an objective extra space dimension. "Particle"…