Related papers: Introducing Multidimensional Dirac-Hestenes Equati…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
Dirac's theorem (1952) is a classical result of graph theory, stating that an $n$-vertex graph ($n \geq 3$) is Hamiltonian if every vertex has degree at least $n/2$. Both the value $n/2$ and the requirement for every vertex to have high…
The $D$-dimensional $(\beta, \beta')$-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. In the D=3 and $\beta=0$ case, the latter…
The Dirac equation may be thought as originating from a theory of five-dimensional (5D) space-time. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time…
We construct Dirac operators and spectral triples for certain, not necessarily self-similar, fractal sets built on curves. Connes' distance formula of noncommutative geometry provides a natural metric on the fractal. To motivate the…
In this article, we study a generalisation of the Seiberg-Witten equations, replacing the spinor representation with a hyperKahler manifold equipped with certain symmetries. Central to this is the construction of a (non-linear) Dirac…
We reanalyze the problem of a 1D Dirac single particle colliding with the electrostatic potential step of height $V_{0}$ with a positive incoming energy that tends to the limit point of the so-called Klein energy zone, i.e., $E\rightarrow…
The authors prove that the dynamics of spin 1/2 particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three…
Special-relativistic dynamically-generated elementary-particle mass is represented by a self-adjoint energy operator acting on a rigged Hilbert space (RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy operator is…
The cycle space $\mathcal{C}(G)$ of a graph $G$ is defined as the linear space spanned by all cycles in $G$. For an integer $k\ge 3$, let $\mathcal{C}_k (G)$ denote the subspace of $\mathcal{C}(G)$ generated by the cycles of length exactly…
In the present paper, we study the Dirac equation in the background of Minkowski space-time on a light cone. With the help of the coupling of the radial parts, the system of 4 equations is reduced to two different second-order differential…
A representation of solutions of the one-dimensional Dirac equation is obtained. The solutions are represented as Neumann series of Bessel functions. The representations are shown to be uniformly convergent with respect to the spectral…
The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…
We consider the Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimised by the isosceles right triangle both under the area or perimeter constraints. 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…
Resonance plays critical roles in the formation of many physical phenomena, and several methods have been developed for the exploration of resonance. In this work, we propose a new scheme for resonance by solving the Dirac equation in…
The semiclassical regime of 2D static Dirac matter is obtained from the Dirac equation in curved space-time. To simplify the formulation, the Cartesian space-time geometry parametrization is transformed to isothermal coordinates using…
We are interested in four-dimensional Dirac-Klein-Gordon equations, a fundamental model in particle physics. The main goal of this paper is to establish global existence of solutions to the coupled system and to explore their long-time…
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…
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…