Representable states on quasi-local quasi *-algebras

TL;DR

This paper investigates the conditions under which local states on quasi-local quasi *-algebras can be combined into a global state, exploring properties of local modifications and their asymptotic behavior.

Contribution

It introduces a framework for analyzing the compatibility of local states to form global states on quasi-local quasi *-algebras, extending previous physics-motivated work.

Findings

Characterization of compatible local states

Analysis of local modifications of states

Insights into asymptotic behavior of states

Abstract

Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a {\em global} state. Some properties of {\em local modifications} of representable states and some aspects of their asymptotic behavior are also considered.