相关论文: Hamiltonian self-adjoint extensions for (2+1)-dime…

The present paper studies the Dirac Hamiltonian of a test electron with a domain of bi-spinor wave functions supported on the static region inside the Cauchy horizon of the subextremal RWN black hole spacetime, respectively inside the event…

We investigate the self-adjointness of the two-dimensional Dirac operator $D$, with quantum-dot and Lorentz-scalar $\delta$-shell boundary conditions, on piecewise $C^2$ domains with finitely many corners. For both models, we prove the…

We study the solutions of the (2+1)-dimensional kappa-deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the…

We study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The…

Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian $H=\frac 12 p_u^2+\alpha(u)L+\beta(u)$ with new canonically conjugated coordinates…

We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic…

The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the…

Effects of fermion-vacuum polarization by a singular configuration of an external static vector field are considered in (2 + 1)-dimensional spacetime. Expressions for the induced vacuum charge and magnetic flux are obtained.

The self-adjoint extension (SAE) procedure is considered in the Schrodinger equation for potentials behaving as an attractive inverse square at the origin of coordinates. This approach guarantees self-adjointness of the radial Hamiltonian…

Singular configuration of an external static magnetic field in the form of a string polarizes vacuum in the secondly quantized theory on a plane which is orthogonal to the string axis. We consider the most general boundary conditions at the…

We consider a linear symmetric operator in a Hilbert space that is neither bounded from above nor from below, admits a block decomposition corresponding to an orthogonal splitting of the Hilbert space and has a variational gap property…

The internal low-energy symmetry of the massless Lorentz-invariant Dirac Hamiltonian in $2+1$ dimensions is known to be $O(2N)$, where $N$ is the number of two-component Dirac fermions. Here we point out that there exists an analogous…

The Hamiltonians of $SU(2)$ and $SU(3)$ gauge theories in 3+1 dimensions can be expressed in terms of gauge invariant spatial geometric variables, i.e., metrics, connections and curvature tensors which are simple local functions of the…

Let $(G,c)$ be an infinite network, and let $\mathcal{E}$ be the canonical energy form. Let $\Delta_2$ be the Laplace operator with dense domain in $\ell^2(G)$ and let $\Delta_{\mathcal{E}}$ be the Laplace operator with dense domain in the…

A system of a Dirac particle interacting with the radiation field is considered. The Hamiltonian of the system is defined by $H = \alpha\cdot(\hat\mathbf{p}-q\mathbf{A}(\hat\mathbf{x}))+m\beta + H_f$ where $q\in\mathbb{R}$ is a coupling…

In the present paper we deal with the issue of finding the self-adjoint extensions of a $p^4$-corrected Hamiltonian. The importance of this subject lies on the application of the concepts of quantum mechanics to the minimal-length scale…

We compute the deficiency spaces of operators of the form $H_A{\hat{\otimes}} I + I{\hat{\otimes}} H_B$, for symmetric $H_A$ and self-adjoint $H_B$. This enables us to construct self-adjoint extensions (if they exist) by means of von…

In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra $\mathfrak{sl}(2|1)$ generated by…

In (3+1) Hamiltonian form, the conditions for the electric/magnetic invariance of generic self-interacting gauge vector actions and the definition of the duality generator are obvious. Instead, (3+1) actions are not intrinsically Lorentz…