Pseudo-unitary dynamics of free relativistic quantum mechanical twofold systems

Abstract

A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably normalized vectors belonging to the two-complex-dimensional spaces that occur in local orthogonal decompositions of isomorphic copies of Cartan’s space. The corresponding dynamical variables thus show up as bounded pseudo-Hermitian operator restrictions that possess real discrete spectra. Any measurement processes have to be performed locally in orthocronous proper Lorentz frames, but typical observational correlations are expressed in terms of symbolic configurations which come from the covariant action on spaces of state vectors of the Poincaré subgroup of an adequate realization of SU(2,2). The overall approach turns out to supply a supposedly natural description of the dynamics of free twofold systems in flat spacetime. One of the main outlooks devised here brings forward the possibility of carrying out methodically the construction of a background to a new relativistic theory of quantum information.