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Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…
The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by the 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are…
The problem of a spin 1 charged particle with electromagnetic polarizability, obeying a generalized 15-component quantum mechanical equation, is investigated in presence of the external Coulomb potential. With the use of the Wigner's…
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 study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials $V$ decaying like $\langle x \rangle ^{-\d}$ at infinity for some $\d >0$. By…
In this work, we propose an efficient and accurate computational method to evaluate the many-potential $\alpha\left(Z\alpha\right)^{n\ge3}$ vacuum polarization density of hydrogen-like atoms within the finite-basis approximation of the…
The spectrum of the Dirac oscillator perturbed by the Coulomb potential is considered. The Regge trajectories for its bound states are obtained with the method of $\hbar$-expansion. It is shown that the split of the degenerate energy levels…
The Coulomb phase of a quantum field theory, when present, illuminates the analysis of its line operators and one-form symmetries. For 4d $\mathcal{N}=2$ field theories the low energy physics of this phase is encoded in the special K\"ahler…
The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting…
We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz potentials. These definitions rely on precise resolvent…
We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kre{\u\i}n-Vi\v{s}ik-Birman extension scheme, or…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
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…
Artificial atoms in graphene hosting a series of quasi-bound states can serve as an excellent platform to explore atomic collapse and become a basis to design novel graphene nanodevices. We theoretically study behaviors of massless Dirac…
We study properties of the zero and near-zero eigenmodes of the overlap Dirac operator in compact U(1) gauge theory. In the confinement phase the exact zero-modes are localized as found by studying the values of the inverse participation…
We show that the eigenvalues of the intrinsic Dirac operator on the boundary of a Euclidean domain can be obtained as the limits of eigenvalues of Euclidean Dirac operators, either in the domain with a MIT-bag type boundary condition or in…
We consider generalised Dirac--Schr\"odinger operators, consisting of a self-adjoint elliptic first-order differential operator D with a skew-adjoint 'potential' given by a (suitable) family of unbounded operators. The index of such an…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
The Dirac-Dolbeault operator for a compact K\"ahler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows to express the values of the sections of the…
The variational approach to QCD in Coulomb gauge developed previously by the T\"ubingen group is improved by enlarging the space of quark trial vacuum wave functionals through a new Dirac structure in the quark-gluon coupling. Our ansatz…