Related papers: Path Integral and Spectral Representations for Sup…
In this paper we formulate our results on the essential spectrum of many-particle pseudorelativistic Hamiltonians without magnetic and external potential fields in the spaces of functions, having arbitrary type $\alpha$ of the permutational…
A non-Hermitian P$_{\phi}$T$_{\phi}$-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians H$_{r}$, H$_{\theta}$, and H$_{\phi}$ play essential roles and offer some user-feriendly…
Invited talk given at the ``International Workshop on `Symmetry Methods in Physics' in memory of Ya.\ A.\ Smorodinsky, 5--10 July 1993, Dubna, Russia; to appear in the proceedings. In this contribution I present further results on steps…
A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpreted as higher-order superintegrable perturbations of the 2D…
We model a single-electron ion (hydrogenic atom) as a static, spherically symmetric electrovacuum spacetime in which the nucleus is treated as a timelike line-singularity and the electron is treated as a test particle following Dirac's…
We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
In the holographic model of Dirac semimetals being the Einstein-Maxwell scalar gravity with the auxiliary $U(1)$-gauge field, coupled to the ordinary Maxwell one by {\it kinetic mixing } term, the black brane response to the electric fields…
In this article we investigate and solve exactly the modified Dirac oscillator in curved spacetime with spin and pseudospin symmetries through an algebraic approach. By focusing on the radial part of this problem, we use the Schr\"odinger…
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…
The purpose of this paper is to make an explicit construction of specific self-adjoint extensions of the Dirac Hamiltonian in the presence of a $\delta$-sphere interaction of finite radius. The exact resolvent kernel of the free Dirac…
We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) symmetry. The approach is based on constructing a Hamiltonian as the…
The identification of pseudospin symmetry as a relativistic symmetry of the Dirac Hamiltonian is used to explain the structure of radial nodes occurring in pseudospin doublets and to illuminate the special status of nodeless intruder states…
We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac…
The superconducting proximity effect on two-dimensional massless Dirac electrons is usually analyzed using a simple model consisting of the Dirac Hamiltonian and an energy-independent pair potential. Although this conventional model is…
The supersymmetric solutions of PT-symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schrodinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired…
We study the spin factor problem both in $3+1$ and $2+1$ dimensions which are essentially different for spin factor construction. Doing all Grassmann integrations in the corresponding path integral representations for Dirac propagator we…
The aim of this work is to find exact solutions of the Dirac equation in 1+1 space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and…
Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted…