Related papers: Eigenvalue estimates for the Dirac operator and ha…

We review some recent results concerning lower eigenvalues estimates for the Dirac operator [6, 7]. We show that Friedrich's inequality can be improved via certain well-chosen symmetric tensors and provide an application to Sasakian spin…

We estimate the behavior of the generalized eigenfunctions of critical Dirac operators (which are Dirac operators with eigenfunctions and/or resonances for $E=m$) plus small perturbations in the potential. The results also apply for other…

This paper has been withdrawn by the authors due to an error.

This paper has been withdrawn at the request of one of the authors.

In this comment we show that the eigenvalues of a quartic anharmonic oscillator obtained recently by means of the asymptotic iteration method may not be as accurate as the authors claim them to be.

In this paper, we introduce q,{\omega}-Dirac system. We investigate the existence and uniqueness of solutions for this system and obtain some spectral properties based on the Hahn difference operator. Also we give two examples, which…

Under various elliptic boundary conditions, we obtain lower eigenvalue estimates for Dirac operators by using Hormander's weighted $L^2$-technique. Lower bounds in terms of the volume of the underlying manifolds are also deduced from the…

Withdrawn due to an incompleteness of the main results.

This paper has been withdrawn by the authors due to need of essential revision.

We derive explicit inequalities for sums of eigenvalues of one-dimensional Schr\"{o}dinger operators on the whole line. In the case of the perturbed harmonic oscillator, these bounds converge to the corresponding trace formula in the limit…

This paper was withdrawn by arXiv admin due to authors' misrepresentation of identity/affiliation.

In this paper, we study the behavior of the eigenvalues of the one and two dimensions of q-deformed Dirac oscillator. The eigensolutions have been obtained by using a method based on the q-deformed creation and annihilation operators in…

The eigenvalue equation has been found for a Hamilton function in a form independent of the choice of a potential. This paper proposes a modified Fedosov construction on a flat symplectic manifold. Necessary and sufficient conditions for…

This paper has been withdrawn by the author(s), due a mistake of factor 1/2.

We give a survey of results relating the restricted holonomy of a Riemannian spin manifold with lower bounds on the spectrum of its Dirac operator, giving a new proof of a result originally due to Kirchberg.

This paper has been withdrawn by the author due to a crucial sign error in equation 1.

We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined Weitzenb\"ock techniques. It applies to manifolds with harmonic curvature tensor and depends on the Ricci tensor.…

The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions…

This paper has been withdrawn by the authors.

This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.