Related papers: Huygens' principle and Dirac-Weyl equation
Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the…
We prove a general version of Egorov's theorem for evolution propagators in the Euclidean space, in the Weyl--H\"ormander framework of metrics on the phase space. Mild assumptions on the Hamiltonian allow for a wide range of applications…
We present preliminary results on a novel numerical method describing wave propagation in non-uniform media. Following Huygens-Fresnel' principle, we model the wavefront as an array of point sources that emit wavelets, which interfere. We…
We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the…
We study the massless limit of the Klein-Gordon (K-G) equation in 1+1 dimensions with static complex potentials as an attempt to give an alternative, but equivalent, representation of plane electromagnetic (em) wave propagation in active…
As an analog model of general relativity, optics on some two-dimensional (2D) curved surfaces has been increasingly paid attention to in the past decade. Here, in light of Huygens-Fresnel principle, we propose a theoretical frame to study…
We consider gravitational radiation in the presence of non-compact extra dimensions. If their number is odd, all spacetime becomes odd-dimensional and formation of gravitational radiation becomes non-trivial because of violation of the…
Due to spectral obstructions, a scattering theory in the Lax-Phillips sense for the wave equation for differential p-forms on H^{n+1} cannot be developed. As a consequence, Huygens' principle for the wave equation in this context does not…
The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2,…
We identify a fundamental space-time invariance principle by combining the thesis of the conventionality of simultaneity with the Hugyens-Fresnel-Miller model of wave propagation. By following the standard gauge prescription, we show that…
In this short note, based on Carleman estimates and Holmgren's type theorems, we provide a converse theorem of the classical Huygens principle for free wave equations. Possible generalizations to other underlying space-times or other wave…
We explore the limits of fractional dispersive effects and their incidence in the propagation of polynomial weights. More precisely, we consider the fractional KdV equation when a differential operator of negative order determines the…
We prove a uniform weighted resolvent estimate for the massless Klein-Gordon operator on a curved spacetime which is sufficiently close to the Minkowski spacetime. This particularly implies the existence and H\"{o}lder continuity of the…
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry…
We present a universal view on diffusive behaviour in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behaviour (Brownian motion with drift) and weak chaos…
Relying on the variational principle, it is proved that new contradictions emerge from an analysis of the Lagrangian density of the Klein-Gordon field: normalization problems arise and interaction with external electromagnetic fields cannot…
We study the particle spectrum and the unitarity of the generic n-dimensional Weyl-invariant quadratic curvature gravity theories around their (anti-)de Sitter [(A)dS] and flat vacua. Weyl symmetry is spontaneously broken in (A)dS and…
In this paper we put forward a viral propagation model with nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential…
The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is…
We derive the uncertainty principle for a Dirac fermion in a torsion field obeying the Hehl-Datta (HD) equation. We first discuss that there should be a correction factor to the Heisenberg uncertainty principle (HUP) when torsional effects…