Related papers: Total angular momentum from Dirac eigenspinors
We study a formulation of euclidean general relativity in which the dynamical variables are given by a sequence of real numbers $\lambda_{n}$, representing the eigenvalues of the Dirac operator on the curved spacetime. These quantities are…
Let $M$ be a closed connected spin manifold of dimension $2$ or $3$ with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric on $M$ the non-harmonic eigenspinors of the Dirac operator are nowhere…
I give some personal remarks on some current issues in the nucleon spin structure study. At an elementary level I propose a new angular momentum separation for the massless Dirac field in a free theory which mimics the usual free photon…
For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined with known lower Dirac eigenvalue estimates, this has a number…
A general spin-resolved momentum distribution of electron-positron pairs produced in strong external fields is derived by combining the covariant spin projection operator and the Dirac-Heisenberg-Wigner (DHW) formalism. The result shows…
Dirac vortices, originally studied in quantum field theories to predict localized zero-energy modes, were recently realized in photonics, leading to Dirac vortex cavities. With topological protection, Dirac vortex cavities offer robust…
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the…
Effects due to fermion-vacuum polarization by an external static magnetic field are considered in a two-dimensional noncompact curved space with a nontrivial topology. An expression for the vacuun angular momentum is obtained. Like the…
The Shishkin's solutions of the Dirac equation in spherical moving frames of the de Sitter spacetime are investigated pointing out the set of commuting operators whose eigenvalues determine the integration constants. It is shown that these…
Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…
Starting from the zero modes of the Dirac-Weyl equation for Landau levels in the symmetric gauge, we propose a novel mechanism to construct the eigenvalues and its eigenfunctions. We show that the problem may be addressed without numerical…
A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free…
Penrose's twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with…
We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a…
We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$.…
The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin…
We give a formula for the first eigenvalue of the Dirac operator acting on spinor fields of a spin compact irreducible symmetric space $G/K$.
The planar dynamics of spin-1/2 quantum relativistic particles is important for several physical systems. In this paper we derive, by a simple method, the generators for the continuous symmetries of the 3+1 Dirac equation for planar motion,…