We consider Dirac operators defined on planar domains. For a large class of boundary
conditions, we give a direct proof of their self-adjointness in the Sobolev space H^ 1 H 1.

The two-dimensional Dirac operator describes low-energy excitations in graphene. Different
choices for the boundary conditions give rise to qualitative differences in the spectrum of the …

We study a self-adjoint realization of a massless Dirac operator on a bounded connected
domain R2 which is frequently used to model graphene. In particular, we show that this …

Consider a Dirac operator defined on the whole plane with a mass term of size m supported
outside a domain $$\Omega $$ Ω . We give a simple proof for the norm resolvent …

We prove tunneling estimates for two-dimensional Dirac systems which are localized in
space due to the presence of a magnetic field. The Hamiltonian driving the motion admits the …

We study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular
to the plane. We focus on the infinite-mass boundary condition (also called MIT bag …

We consider a (semi-)relativistic spin-1/2 particle interacting with quantized radiation. The
Hamiltonian has the form $\hat{H}_c^V:=\{c^2[(\mathbf{p}+{\bf A})^2+{\bf \sigma}\cdot{\bf B}]+(…

We study the Hartree–Fock model for pseudorelativistic atoms, that is, atoms where the kinetic
energy of the electrons is given by the pseudo-relativistic operator $$\sqrt{(|{\bf p}|c)^{2} + (…

We prove an HVZ theorem for a general class of no-pair Hamiltonians describing an atom
or positively charged ion with several electrons in the presence of a classical external …

This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on
a bounded open set with Dirichlet conditions on the boundary. Assuming that the magnetic …