Related papers: The Dirac equation in D-dimensional spherically sy…
The Dirac equation is generalized to $D+1$ space-time.The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd $D$ and even $D$ cases. The…
A supersymmetric analysis is presented for the d-dimensional Dirac equation with central potentials under spin-symmetric (S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct the explicit shift operators that are…
This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods.…
We extend a previously successful discussion of the constrained Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a…
In this article we develop energy methods for a large class of linear and nonlinear Dirac-type equations in two-dimensional Minkowski space. We will derive existence results for several Dirac-type equations originating in quantum field…
We calculate all symmetries of the Dirac-Pauli equation in two-dimensional and three-dimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of…
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…
By requiring unambiguous symmetric quantization leading to the Dirac equation in a curved space, we obtain a special representation of the spin connections in terms of the Dirac gamma matrices and their space-time derivatives. We also…
Consider the Schr\"{o}dinger operator $H = -\Delta + V$, where the potential $V$ is real, $\mathbb{Z}^2$-periodic, and additionally invariant under the symmetry group of the square. We show that, under typical small linear deformations of…
We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and…
The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein…
We generalize previous works on the Dirac eigenvalues as dynamical variables of the Euclidean gravity and N=1 D=4 supergravity to on-shell N=2 D=4 Euclidean supergravity. The covariant phase space of the theory is defined as as the space of…
We study the spectrum of spherically symmetric Dirac operators in three-dimensional space with potentials tending to infinity at infinity under weak regularity assumptions. We prove that purely absolutely continuous spectrum covers the…
The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing…
We generalize the method of obtaining the fundamental linear partial differential equations such as the diffusion and Schrodinger equation, Dirac and telegrapher's equation from a simple stochastic consideration to arrive at certain…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
In the present article we solve, via separation of variables, the massless Dirac equation in a nonstationary rotating, causal G\"odel-type cosmological universe, having a constant rotational speed in all the points of the space. We compute…
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…
It is shown how can be derived the normalized energy eigenspinors of the free Dirac field on anti-de Sitter spacetime, by using a Cartesian tetrad gauge where the separation of spherical variables can be done like in special relativity.
An elementary treatment of the Dirac equation in the presence of a three dimensional spherically symmetric delta potential is presented. We show how to calculate the cross section using the relativistic wave expansion method for a one delta…