Spectral analysis of the massless Dirac operator on a 3-manifold

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Spectral theoretic characterization of the massless Dirac operator

We consider an elliptic self-adjoint first-order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact three-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squares of Euclidean norms of eigenfunctions evaluated at a given point of the...

Spectral asymmetry of the massless Dirac operator on a 3 - torus

Dimensional Reduction of Dirac Operator

We elaborate an explicit example of dimensional reduction of the free massless Dirac operator with SU(3)-symmetry, defined on 12-dimensional manifold, which is the total space of principle SU(3)-bundle over 4-dimensional manifold. It turns out that after the dimensional reduction we obtain the “usual” Dirac operator, defined on 4-dimensional pseudo-Riemannian (non-flat) manifold but with mass t...

0 Eigenvalue Distributions of the QCD Dirac Operator

We compute by Monte Carlo methods the individual distributions of the kth smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge theory with staggered fermions. Very precise agreement is found in all cases. As a simple by-product we also extract the microscopic spectral density of the Dir...