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

Abstract. 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.