Related papers: Eigenvalue estimates for the Dirac operator and ha…
We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays $a_1$ and $a_2$ not less than one-third of the interval. It has been proved that the operator can be recovered…
At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic)…
This paper has been withdrawn by the author due to incomplete interpretation for the results.
We review some recent results on eigenvalues of fractional Laplacians and fractional Schr\"odinger operators. We discuss, in particular, Lieb-Thirring inequalities and their generalizations, as well as semi-classical asymptotics.
Let $$L_0=\suml_{j=1}^nM_j^0D_j+M_0^0,\,\,\,\,D_j=\frac{1}{i}\frac{\pa}{\paxj}, \quad x\in\Rn,$$ be a constant coefficient first-order partial differential system, where the matrices $M_j^0$ are Hermitian. It is assumed that the homogeneous…
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 determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…
A generalized two-dimensional periodic Dirac operator is considered, with $L^{\infty}$-matrix-valued coefficients of the first order derivatives and with complex matrix-valued potential. It is proved that if the matrix-valued potential has…
We compute the chiral condensate in 2+1-flavor QCD through the spectrum of low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique…
By decision of the first author, the paper will no longer be available.
We study the behavior of the spectrum of the Dirac operator on collapsing S^1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.
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…
We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal…
In this paper we present a summarizing description of the connection between Dirac operators on conformally flat manifolds and automorphic forms based on a series of joint work with John Ryan over the last fifteen years. We also outline…
It is shown that theories already presented as rigorous mathematical formalizations of widespread manipulations of Dirac's delta function are all unsatisfactory, and a new alternative is proposed.
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…
In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schr\"{o}dinger operator to the Dirac operator, imposing some suitable rigidity conditions on the matricial structure of the potential,…
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real and discrete, we show that the eigenfunctions do not form a…
This paper has been withdrawn by the author.
It is popular to discuss low energy physics in lattice gauge theory in terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra.