Related papers: Massless Dirac equation on spinor bundles over rea…
We develop the potential scattering of a spinor within the context of perturbation field theory. As an application, we reproduce, up to second order in the potential, the diffusion results for a potential barrier of quantum mechanics. An…
Starting with the Dirac equation outside the event horizon of a non-extreme Kerr black hole, we develop a time-dependent scattering theory for massive Dirac particles. The explicit computation of the modified wave operators at infinity is…
We consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings: $F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$, where the…
We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish…
A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
We assume that the manifold with boundary, X, has a Spin_C-structure with spinor bundle S. Along the boundary, this structure agrees with the structure defined by an infinite order integrable almost complex structure and the metric is…
The disclination in Lorentz space-time is studied in detail by means of topological properties of $\phi $-mapping. It is found the space-time disclination can be described in term of a Dirac spinor. The size of the disclination, which is…
This note tackles the problem of the backscattering of a mass-less scalar field in the case of Schwarzschildean space-time. It shows that the effect depends both on a distance from the horizon and on the wave length. The obtained estimates…
We consider the wave equation on a manifold $(\Omega,g)$ of dimension $d\geq 2$ with smooth strictly convex boundary $\partial\Omega\neq\emptyset$, with Dirichlet boundary conditions. We construct a sharp local in time parametrix and then…
Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and…
In [16], we established Trudinger-Moser inequalities for complete noncompact Riemannian manifold on which the Ricci curvature has lower bound and the injectivity radius is strictly positive. In this note, we improve those inequalties when…
We prove dispersive and Strichartz estimates for Schr\"o- dinger equations on a class of locally symmetric spaces {\Gamma}\X, where X = G/K is a symmetric space and {\Gamma} is a torsion free discrete sub- group of G. We deal with the cases…
We discuss the problem of canonical quantization of a free massive spinor field in the Schwarzschild spacetime. It is shown that a consistent procedure of canonical quantization of the field can be carried out without taking into account…
The massive scalar field theory and the chiral Schwinger model are quantized on a Poincar\'e disk of radius $\rho$. The amplitudes are derived in terms of hypergeometric functions. The behavior at long distances and near the boundary of…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
We present some results obtained in collaboration with prof. Piero D'Ancona concerning global existence for the 3D cubic non linear massless Dirac equation with a potential for small initial data in $H^1$ with slight additional assumptions.…
Using spinorial techniques, we prove, for a class of pseudo-hyperbolic ambient manifolds, a Heintze-Karcher type inequality. We then use this inequality to show an Alexandrov type theorem in such spaces.
We investigate the influence of the temporal variations of various medium parameters on the propagation of Dirac-type waves in materials where the quasiparticles are described by a generalized version of the pseudospin-1/2 Dirac equation.…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.