Related papers: Eigenspaces of the Spin Dirac operator over S^3

This seminal paper marks the beginning of our investigation into on the spectral theory based on $S$-spectrum applied to the Dirac operator on manifolds. Specifically, we examine in detail the cases of the Dirac operator $\mathcal{D}_H$ on…

In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…

We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].

We show that for generic Riemannian metrics on a closed spin manifold of dimension three the Dirac operator has only simple eigenvalues.

We construct a universal spin$_c$ Dirac operator on $\mathbb{C}P^n$ built by projecting $su(n+1)$ left actions and prove its equivalence to the standard right action Dirac operator on $\mathbb{C}P^n$. The eigenvalue problem is solved and…

The matrix elements of the spin operator for the periodic Ising model in a basis of eigenvectors for the transfer matrix are calculated in the massive scaling limit.

The vector space $V^k$ of the eigenfunctions of the Laplacian on the three sphere $S^3$, corresponding to the same eigenvalue $lambda_k = -k (k +2)$, has dimension $(k + 1)^2$. After recalling the standard bases for $V^k$, we introduce a…

Two numerical algorithms for the computation of eigenvalues of Dirac operators in lattice gauge theories are described: one is an accelerated conjugate gradient method, the other one a standard Lanczos method. Results obtained by Cullum's…

This paper reviews some recent work on (s)pin structures and the Dirac operator on hypersurfaces (in particular, on spheres), on real projective spaces and quadrics. Two approaches to spinor fields on manifolds are compared. The action of…

We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…

Spin 1 particle is investigated in 3-dimensional curved space of constant positive curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin-Kemmer equation in quasi…

We determine the spectrum of Kostant's cubic Dirac operator $D^{1/3}$ on locally symmetric Lorentzian manifolds of the form $\Gamma\backslash {\rm Osc}_1$, where ${\rm Osc}_1$ is the four-dimensional oscillator group and $\Gamma\subset {\rm…

In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this…

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and…

We introduce a new method for computing spectra of molecules for which a spin-spin term in the Hamiltonian has an important effect. In previous calculations, matrix elements of the spin-spin term and of the potential were obtained by…

With the Schwinger model as example I discuss properties of lattice Dirac operators, with some emphasis on Monte Carlo results for topological charge, chiral fermions and eigenvalue spectra.

We consider quantum mechanical systems of spin chain type, with finite-dimensional Hilbert spaces and $\mathcal{N}=2$ or $\mathcal{N}=4$ supersymmetry, described in $\mathcal{N}=2$ superspace in terms of nonlinear chiral multiplets. We…

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\in\Lambda^3M$ by means of twistor theory. An optimal lower bound for the first eigenvalue of the Dirac…