Related papers: Fundamental solutions for the Dirac equation in cu…
The equation of the spin-$\frac{1}{2}$ particles in the Friedmann-Lema\^itre-Robertson-Walker spacetime is investigated. The retarded and advanced fundamental solutions to the Dirac operator and generalized Dirac operator as well as the…
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 discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated…
We give a local integral formula, valid on general curved space-times, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin using the method developed by Friedlander in his book "the wave equation on a curved…
The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in the space of constant positive curvature, spherical Riemann space, in presence of an external magnetic field, analogue of the…
In this paper, we study the Cauchy and Goursat problems of the spin-$n/2$ zero rest-mass equations on Minkowski spacetime by using the conformal geometric method. In our strategy, we prove the wellposedness of the Cauchy problem in…
With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant…
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…
In the paper we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler--Poisson--Darboux equation with Bessel operators via generalized translation and spherical mean operators for…
In this paper, we consider the Cauchy problem of Dirac equations with Chern-Simons-Proca (CSP) gauge field. We investigate global well-posedness and scattering theory for the solutions with small initial data. The main difficulties come…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
We consider the Euler--Darboux equation with parameters modulo 1/2 and generalization to the space 3D analogue. Due to the fact that the Cauchy problem in its classical formulation is incorrect for such parameter values, the authors propose…
We deal with the Cauchy problem for the space-time fractional diffusion-wave equation, which is obtained from the standard diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in…
The Cauchy problem for the massive Dirac equation is studied in the Reissner-Nordstr\"om geometry in horizon-penetrating Eddington-Finkelstein-type coordinates. We derive an integral representation for the Dirac propagator involving the…
The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
The Dirac equation is solved in the rotating Bertotti-Robinson spacetime. The set of equations representing the Dirac equation in the Newman-Penrose formalism is decoupled into an axial and angular part. The axial equation, which is…
We find out classical particles, starting from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. We recover the results by Mathisson-Papapetrou, hence establishing a…
We give an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an integral representation for smooth compactly supported functions which in turn we use…