TL;DR
This paper introduces a framework for joinings of C*-dynamical systems using free products, explores disjointness properties, and connects multi-time correlation functions in quantum statistical mechanics to this framework.
Contribution
It develops a novel approach to joinings of C*-dynamical systems via free products and relates it to quantum statistical mechanics.
Findings
Defined joinings using free products of C*-algebras
Analyzed disjointness for ergodic and identity systems
Connected multi-time correlation functions to the joining framework
Abstract
Joinings of C*-dynamical systems are defined in terms of free products of C*-algebras, as an analogue of joinings of classical dynamical systems. We then consider disjointness in this context, in particular for ergodic versus identity systems. Lastly we show how multi-time correlation functions appearing in quantum statistical mechanics naturally fit into this joining framework.
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