Representations and derivations of quasi *-algebras induced by {\em local modifications} of states

TL;DR

This paper explores how local modifications of states in quasi *-algebras influence their GNS representations and the associated derivations, shedding light on the dynamics of quantum systems with infinite degrees of freedom.

Contribution

It provides a detailed analysis of the relationship between GNS representations and local state modifications in quasi *-algebras, and their impact on derivations and quantum dynamics.

Findings

Local modifications affect the spatiality of derivations.

GNS representations of locally modified states are closely related.

Implications for the dynamics of infinite quantum systems.

Abstract

The relationship between the GNS representations associated to states on a quasi *-algebra, which are {\em local modifications} of each other (in a sense which we will discuss) is examined. The role of local modifications on the spatiality of the corresponding induced derivations describing the dynamics of a given quantum system with infinite degrees of freedom is discussed.