We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann’s theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the...

Let M be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of M , and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group Z2 , we give a very simple expression for the multiplicities of eigenvalues that allows t...

Three dimensional topological Dirac semi-metals represent a novel state of quantum matter with exotic electronic properties, in which a pair of Dirac points with the linear dispersion along all momentum directions exist in the bulk. Herein, by using the first principles calculations, we discover a new metastable allotrope of Ge and Sn in the staggered layered dumbbell structure, named as german...

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to ±∞ or there are eigenvalues converging to those of the torus. This is shown to be true in general for collapsing circle bundles with totally geodesic fibers. Using the Hopf fibration we use this...

The Dirac equation plays a key role in microscopic descriptions of many-fermion systems, employing covariant density functional theory and the relativistic mean-field approach. In application to nuclei and hadrons, the required Dirac mean-field Hamiltonian involves a mixture of Lorentz vector and scalar potentials. Recently, symmetries of Dirac Hamiltonians with such Lorentz structure were show...

In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian primary constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints which is a new feature in the context of constrained systems. We discuss the Dirac brackets and the reduced phase space structure for different boundary conditio...

Consider a flat symplectic manifold (M, ω), l ≥ 2, admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If λ is an eigenvalue of the symplectic Dirac operator such that −ılλ is not a symplectic Killing numbe...

where the field strength γ = Ze and e ≈ 1/137.04 the fine structure constant. xk = |xk| is the modulus of the spatial coordinate of electron k, k = 1, 2. The momentum of electron k is denoted by pk, and β, α = (α1, α2, α3) and σ = (σ1, σ2, σ3) are the Dirac and Pauli matrices, respectively. Due to the positron degrees of freedom the spectrum of the Coulomb-Dirac operator is unbounded from below...

A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus. Abstract We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of...

The ”Fixed Point Dirac Operator” and ”Chirally Improved Fermions” both use large numbers of gauge paths and the full Dirac structure to approximate a solution of the Ginsparg-Wilson equation. After a brief review of the two approaches we present recent results for quenched QCD with pion masses down to 210 MeV. We discuss the limits and advantages of approximate parameterizations and outline fut...