Related papers: The Dirac-Klein-Gordon system in the strong coupli…
We establish global existence and derive sharp pointwise decay estimates of solutions to cubic Dirac and Dirac-Klein-Gordon systems on a curved background, close to the Minkowski spacetime. By squaring the Dirac operator, we reduce the…
In this paper we prove well posedness for a system coupling a nonlinear Dirac with a Klein-Gordon equation that represents a toy model for the Helium atom with relativistic corrections: the wave function of the electrons interacts with an…
There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies…
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field…
We construct new relativistic linear differential equation in $d$ dimensions generalizing Dirac equation by employing the Clifford algebra of the cubic polynomial associated to Klein-Gordon operator multiplied by the mass parameter. Unlike…
Compatibility of symmetric quantization of the Dirac equation in a curved space with general covariance gives a special representation of the spin connections in which their dot product with the Dirac gamma matrices becomes equal to the…
We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…
A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the…
We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary…
An effective approach for solving the three-dimensional Dirac equation for spherically symmetric local interactions, which we have introduced recently, is reviewed and consolidated. The merit of the approach is in producing Schrodinger-like…
In this paper, we study the persistence of spatial analyticity for the solutions to the Klein-Gordon-Schr\"{o}dinger system, which describes a physical system of a nucleon field interacting with a neutral meson field, with analytic initial…
We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial data, enabling us to handle initial data that were not…
In the present paper, we study the semi-classical approximation of a Yukawa-coupled massive Dirac-Klein-Gordon system with some general nonlinear self-coupling. We prove that for a constrained coupling constant there exists a family of…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$ converges in the strong resolvent sense to the Hamiltonian…
We consider the Einstein-Dirac system for a massive field, which describes the evolution of self-gravitating massive spinor fields, and we investigate the global evolution problem, when the initial data set is sufficiently close to data…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
In this paper, we investigate the characteristic initial value problem for the Einstein-Dirac system, a model governing the interaction between gravity and spin-$1/2$ fields. We apply Luk's strategy \cite{Luk12} and prove a semi-global…