Pseudo-Unitary Dynamics of Free Relativistic Quantum Mechanical Twofold Systems

TL;DR

This paper develops a pseudo-unitary framework for describing free relativistic quantum particles, providing a novel approach that integrates local Lorentz frames and covariant symmetries, with potential applications in quantum information theory.

Contribution

It introduces a finite-dimensional pseudo-unitary model for relativistic quantum systems, unifying local measurements and covariant symmetries in a new theoretical framework.

Findings

States are represented as normalized vectors in two-complex-dimensional spaces.

Dynamical variables are bounded pseudo-Hermitian operators with real spectra.

The approach suggests a foundation for a relativistic quantum information theory.

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 Poincar\'e 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.