arXiv subjects
Publications and source records attributed to José M. Gracia-Bondía.
The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently be obtained by minimizing the ground-state energy.
Vacuum polarization in external fields is treated by way of calculating - exactly and then perturbatively - the phase of the quantum scattering matrix in the Shale-Stinespring approach to field theory. The link between the Shale-Stinespring method and the Epstein-Glaser renormalization procedure is highlighted.
We address one of the open problems in quantization theory recently listed by Rieffel. By developping in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict, flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view.