Spectral enclosures for Dirac operators perturbed by rigid potentials

Spectral Analysis of Relativistic Atoms – Dirac Operators with Singular Potentials

This is the first part of a series of two papers, which investigate spectral properties of Dirac operators with singular potentials. We examine various properties of complex dilated Dirac operators. These operators arise in the investigation of resonances using the method of complex dilations. We generalize the spectral analysis of Weder [50] and Šeba [46] to operators with Coulomb type potenti...

Dirac Operators and Spectral Geometry

Dirac operators coupled to vector potentials.

Characteristic classes for the index of the Dirac family [unk](A) are computed in terms of differential forms on the orbit space of vector potentials under gauge transformations. They represent obstructions to the existence of a covariant Dirac propagator. The first obstruction is related to a chiral anomaly.

Discrete spectral triples converging to dirac operators

We exhibit a series of discrete spectral triples converging to the canonical spectral triple of a finite dimensional manifold. Thus we bypass the non-go theorem of Gökeler and Schücker. Sort of counterexample. In [2] Connes gave the most general example of non commutative manifolds defined from finite spectral triples, and such discrete manifolds were classified independently by Krajewsky [5, 6...

Perturbed Coulombic potentials in Dirac and Klein-Gordon equations

A relativistic extension of our pseudo-shifted l–expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical integration data.