Consistent relativistic Quantum Theory for systems/particles described by non-Hermitian Hamiltonians and Lagrangians

A causal, non-Hermitian, renormalizable, local, unitary and Lorentz convariant formulation of Quantum Theory (QT) (= Quantum Mechanics (QM) and Quantum Field Theory (QFT)) is developed which is free of formalistic problems we face in the commonly used Hermitian formulation of QT. Side effects of the new formulation of QT are the derivation of a consistent (anti)causal neutrino Lagrangian, the enrichment of chiral symmetries, the removal of the Dirac sea, the separation of positive and negative energy states including a reformulation of the anti-particle concept and a critical analysis of the concept of probability currents. In a first step we apply the new formulation of QT to establish a relation between perturbative Quantum Chromodynamics (QCD) and the (axial)vector meson extended Quark-Level Linear Sigma Model (QLLSM) at high energies.Comment: 14 pages, no figures; invited contribution to the 2nd Int. Workshop on "Hadron Physics, Effective Theories of Low Energy QCD", CFT, Coimbra University, Portugal, September 25-29, 2002; ref. 15 update

On Scalar Meson Dominance in Semi- and Non-Leptonic Weak Pseudoscalar Meson Decays

Aspects of Scalar Meson Dominance in semi- and non-leptonic weak pseudoscalar meson decays are shortly discussed on the basis of the Quark-Level Linear Sigma Model.Comment: 5 pages, no figures, contribution to XI Int. Conf. on "Hadron Spectroscopy" (HADRON 05), 21.-26.8.2005, Rio de Janeiro, Brazi

The Light and Heavy Scalars in Unitarized Coupled Channel and Lagrangian Approaches

Using ideas underlying the flavour-blind "Nijmegen Unitarised Meson Model" we try to understand on the basis of a system of Schroedinger equations with one meson-meson and one (spinless) quark-antiquark channel coupled by a simple delta-shell transition potential the formation of (e.g. scalar) meson-meson scattering singularities in the complex momentum and energy plane. Surprisingly we are able to describe without direct meson-meson interaction and without any need for glueballs the whole known scalar meson spectrum. "Light" scalar mesons (e.g. f0(600), kappa(800), f0(980), a0(985), D*0(2290), ...) are identified to belong to the spectrum of the transition potential, while "heavy" scalars (e.g. f0(1370), K*0(1430), f0(1500), f0(1710), a0(1450), D*0(2621) (?), D*0(2825) (?), D*sJ(2928) (?), ...) are related to the confinement spectrum. Due to the particular value of the charm-strange reduced quark mass level-(anti)crossing in the complex momentum plane occurs which relates the BABAR state Ds(2317) to the bare groundstate of the confinement spectrum, while the respective groundstate of the transition potential ends up as D*sJ(2782) (?). We conclude with a short comment on (our) recent progress in the consistent quantum field theoretical effective description of resonances within a Lagrangian framework.Comment: 5 pages, 1 figure consisting of 4 eps-files; contribution to the 10th Int. Conference on "Hadron Spectroscopy" (HADRON '03), Aschaffenburg, Germany, 31.8.-6.9.200