Dirac operators coupled to vector potentials

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.

Absolutely Continuous Spectrum of Dirac Operators with Square Integrable Potentials

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (−∞,−1] ∪ [1,∞). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a ...

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

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...