Renormalization and Universality of Van der Waals forces

Renormalization ideas can profitably be exploited in conjunction with the superposition principle of boundary conditions in the description of model independent and universal scaling features of the singular and long range Van der Waals force between neutral atoms. The dominance of the leading power law is highlighted both in the scattering as well as in the bound state problem. The role of off-shell two-body unitarity and causality within the Effective Field Theory framework on the light of universality and scaling at low energies is analyzed.Comment: 10 pages, 9 figures. Presented at 19th International IUPAP Conference On Few-Body Problems In Physics (FB 19) 31 Aug - 5 Sep 2009, Bonn, German

Renormalization of One Meson Exchange Potentials and Their Currents

The Nucleon-Nucleon One Meson Exchange Potential, its wave functions and related Meson Exchange Currents are analyzed for point-like nucleons. The leading Nc contributions generate a local and energy independent potential which presents 1/r^3 singularities, requiring renormalization. We show how invoking suitable boundary conditions, neutron-proton phase shifts and deuteron properties become largely insensitive to the nucleon substructure and to the vector mesons. Actually, reasonable agreement with low energy data for realistic values of the coupling constants (e.g. SU(3) values) is found. The analysis along similar lines for the Meson Exchange Currents suggests that this renormalization scheme implies tremendous simplifications while complying with exact gauge invariance at any stage of the calculation.Comment: Talk given at 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2010), Williamsburg, Virginia, 31 May - 4 Jun 201

k-Plane Constant Curvature Conditions

This research generalizes the two invariants known as constant sectional curvature (csc) and constant vector curvature (cvc). We use k-plane scalar curvature to investigate the higher-dimensional analogues of these curvature conditions in Riemannian spaces of arbitrary finite dimension. Many of our results coincide with the known features of the classical k=2 case. We show that a space with constant k-plane scalar curvature has a uniquely determined tensor and that a tensor can be recovered from its k-plane scalar curvature measurements. Through two example spaces with canonical tensors, we demonstrate a method for determining constant k-plane vector curvature values, as well as the possibility of a connected set of values. We also generate loose bounds for candidate values based on sectional curvatures. By studying these k-plane curvature invariants, we can further characterize model spaces by generating basis-independent numbers for various subspaces