Related papers: Self-adjointness of the 2D Dirac operator with sin…

We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the…

In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…

In this article we develop a systematic approach to treat Dirac operators $A_{\eta, \tau, \lambda}$ with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths $\eta, \tau, \lambda \in \mathbb{R}$,…

In this paper the approximation of Dirac operators with general $\delta$-shell potentials supported on $C^2$-curves in $\mathbb{R}^2$ or $C^2$-surfaces in $\mathbb{R}^3$, which may be bounded or unbounded, is studied. It is shown under…

A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…

Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac…

We study correlation functions of scalar operators on the boundary of the $AdS_3$ space deformed by moving massive particles in the context of the AdS/CFT duality. To calculate two-point correlation functions we use the geodesic…

Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by a variational principle that involves only the domain of the symmetric operator.…

We study a self-adjoint realization of a massless Dirac operator on a bounded connected domain $\Omega\subset \mathbb{R}^2$ which is frequently used to model graphene quantum dots. In particular, we show that this operator is the limit, as…

We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_{\omega,\lambda}:=\begin{bmatrix}-\frac{\lambda+\omega}{x}&-\partial_x \\ \partial_x & -\frac{\lambda-\omega}{x}\end{bmatrix}$.…

This paper develops a chiral adelic operator framework in which the functional--equation symmetry of global $L$--functions is realized directly in the spectrum of a Dirac--type Hamiltonian. Working on the id\`ele class space, we place a…

We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model…

We study a natural Dirac operator on a Lagrangian submanifold of a K\"ahler manifold. We first show that its square coincides with the Hodge-de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and…

We present an explicit two-parameter family of finite-band Jacobi elliptic potentials for a non-self-adjoint Dirac operator which connects two previously known limiting cases in which the elliptic parameter is zero or one. A full…

We discuss a discrete analogue of the Dirac-K\"{a}hler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…

Schr\"{o}dinger operators of the form $\Delta - W$ on $L^2_{\text{rad}}(\mathbb{R}^3)$, the space of radially symmetric square integrable functions are relevant in a variety of physical contexts. The potential $W$ is taken to be radially…

We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner…

We give a precise and complete description on the spectrum for a class of non-self-adjoint quasi-periodic operators acting on $\ell^2(\mathbb{Z}^d)$ which contains the Sarnak's model as a special case. As a consequence, one can see various…

We consider Schr\"odinger operators on possibly noncompact Riemannian manifolds, acting on sections in vector bundles, with locally square integrable potentials whose negative part is in the underlying Kato class. Using path integral…