16,423 research outputs found
Electromagnetic Klein-Gordon and Dirac equations in scale relativity
We present a new step in the foundation of quantum field theory with the
tools of scale relativity. Previously, quantum motion equations (Schr\"odinger,
Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written
with a quantum-covariant derivative operator. Then, the nature of gauge
transformations, of gauge fields and of conserved charges have been given a
geometric meaning in terms of a scale-covariant derivative tool. Finally, the
electromagnetic Klein-Gordon equation has been recovered with a covariant
derivative constructed by combining the quantum-covariant velocity operator and
the scale-covariant derivative. We show here that if one tries to derive the
electromagnetic Dirac equation from the Klein-Gordon one as for the free
particle motion, i.e. as a square root of the time part of the Klein-Gordon
operator, one obtains an additional term which is the relativistic analog of
the spin-magnetic field coupling term of the Pauli equation. However, if one
first applies the quantum covariance, then implements the scale covariance
through the scale-covariant derivative, one obtains the electromagnetic Dirac
equation in its usual form. This method can also be applied successfully to the
derivation of the electromagnetic Klein-Gordon equation. This suggests it rests
on more profound roots of the theory, since it encompasses naturally the
spin-charge coupling.Comment: 14 pages, no figure
Dirac Equation in Scale Relativity
The theory of scale relativity provides a new insight into the origin of
fundamental laws in physics. Its application to microphysics allows to recover
quantum mechanics as mechanics on a non-differentiable (fractal) space-time.
The Schr\"odinger and Klein-Gordon equations have already been demonstrated as
geodesic equations in this framework. We propose here a new development of the
intrinsic properties of this theory to obtain, using the mathematical tool of
Hamilton's bi-quaternions, a derivation of the Dirac equation, which, in
standard physics, is merely postulated. The bi-quaternionic nature of the Dirac
spinor is obtained by adding to the differential (proper) time symmetry
breaking, which yields the complex form of the wave-function in the
Schr\"odinger and Klein-Gordon equations, the breaking of further symmetries,
namely, the differential coordinate symmetry () and the parity and time reversal symmetries.Comment: 33 pages, 4 figures, latex. Submitted to Phys. Rev.
Analogy electromagnetism-acoustics: Validation and application to local impedance active control for sound absorption
An analogy between electromagnetism and acoustics is presented in 2D. The
propagation of sound in presence of absorbing material is modeled using an open
boundary microwave package. Validation is performed through analytical and
experimental results. Application to local impedance active control for free
field sound absorption is finally described
Electrophoretic silica-coating process on a nano-structured copper electrode
A method for silica-coating at the nanoscale by electrophoretic deposition is presented here, using raw or grafted silica dispersions
Building profile reconstruction using TerraSAR-X data time-series and tomographic techniques
This work aims to show the potentialities of SAR Tomography (TomoSAR) techniques for the 3-D characterization (height, reflectivity, time stability) of built-up areas using data acquired by the satellite sensor TerraSAR-X. For this purpose 19 TerraSAR-X single-polarimetric multibaseline images acquired over Paris urban area have been processed applying classical nonparametric (Beamforming and Capon) and parametric (MUSIC) spectral estimation techniques
Separable solutions of some quasilinear equations with source reaction
We study the existence of singular separable solutions to a class of
quasilinear equations with reaction term. In the 2-dim case, we use a dynamical
system approach to construct our solutions.Comment: 34 page
Anderson Localization of Matter Waves in 3D Anisotropic Disordered Potentials
Using a cutoff-free formulation of the coherent transport theory, we show
that the interference terms at the origin of localization strongly affect the
transport anisotropy. In contrast to the common hypothesis, we then find that
the anisotropies of incoherent and coherent diffusion are significantly
different, in particular at criticality. There, we show that the coherent
transport anisotropy is mainly determined by the properties of the
disorder-averaged effective scattering medium while the incoherent transport
contributions become irrelevant
Boundary singularities of positive solutions of some nonlinear elliptic equations
We study the behaviour near a boundary point a of any positive solution of a
nonlinear elliptic equations with forcing term which vanishes on the boundary
except at a. Our results are based upon a priori estimates for solutions and
existence or non existence and uniqueness results for solutions of some
nonlinear elliptic equations on the half unit sphere.Comment: 6 page
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