Related papers: Dispersive and Strichartz estimates for Dirac equa…
Distributional sources of cosmic walls crossed by cosmic strings from Riemann-Cartan (RC) Geometry. The matter density of the planar wall is maximum at the point where the cosmic string crosses the cosmic wall. Cartan torsion is has a…
Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of…
We investigate the general properties of the dimensional reduction of the Dirac theory, formulated in a Minkowski spacetime with an arbitrary number of spatial dimensions. This is done by applying Hadamard's method of descent, which…
We establish global well-posedness and scattering for the cubic Dirac equation for small data in the critical space $H^1(\mathbb{R}^3)$. The main ingredient is obtaining a sharp end-point Strichartz estimate for the Klein-Gordon equation.…
We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of…
We propose a modification of the partial wave approach to deal with the relativistic quantum scattering of bosonic and fermionic particles in a class of models concerning gravitating cosmic string spacetimes. These spacetimes are…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix…
The lowest order contribution of the amplitude of the Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on…
The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator…
We examine the structure of spacetime symmetries of toroidally compactified string theory within the framework of noncommutative geometry. Following a proposal of Frohlich and Gawedzki, we describe the noncommutative string spacetime using…
We investigate scaling and correlations of the energy and momentum in an evolving network of cosmic strings in Minkowski space. These quantities are of great interest, as they must be understood before accurate predictions for the power…
We consider the Dirac Operator acting on the Clifford Algebra ${C\ell}_{m}$. We show that under critical assumptions on the potential and the spinor field the equation is subject to an integrability by compensation phenomenon and has a…
We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of…
Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions…
In this paper we consider Dirac operators in $\mathbb R^n$, $n\geq2$, with a potential $V$. Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the operator, we prove a limiting absorption principle for the…
Localization of relativistic particles have been of great research interests over many decades. We investigate the time evolution of the Gaussian wave packets governed by the one dimensional Dirac equation. For the free Dirac equation, we…
In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters. Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in…
The Dirac sea is calculated in an expansion around the light cone. The method is to analyze the perturbation expansion for the Dirac sea in position space. This leads to integrals over expressions containing distributions which are singular…
A Duistermaat-Guillemin-Gutzwiller trace formula for Dirac-type operators on a globally hyperbolic spatially compact stationary spacetime is achieved by generalising the recent construction by Strohmaier and Zelditch [Adv. Math.…