Achronal Localization, Representations of the Causal Logic for massive systems

TL;DR

This paper extends the concept of localization for relativistic quantum particles to achronal regions in Minkowski spacetime, ensuring causality and providing new representations of causal logic for systems with positive mass spectrum.

Contribution

It introduces achronal localization as a causality-compliant framework and constructs novel representations of causal logic for massive quantum systems.

Findings

Achronal localization automatically satisfies causality principles.

Constructed new representations of causal logic for systems with positive mass spectrum.

Established equivalence between achronal localization and causal logic regions.

Abstract

On plain physical grounds localization of relativistic quantum particles is extended to the achronal regions of Minkowski spacetime. Achronal localization fulfills automatically the requirements of causality. It constitutes the frame which complies most completely with the principle of causality for quantum mechanical systems. Achronal localization is equivalent to the localization in the regions of the causal logic. Representations of the causal logic are constructed for the systems with mass spectrum of positive Lebesgue measure and every definite spin. Apparently no representation of the causal logic for a real mass system has been achieved in the past.