Challenges for extensions of the process matrix formalism to quantum field theory

TL;DR

This paper examines the significant challenges and open problems in extending the process matrix formalism from finite-dimensional systems to quantum field theory, highlighting the complexity of such a transition.

Contribution

It provides a comprehensive overview of the conceptual and technical issues involved in generalizing the process matrix formalism to quantum field theory.

Findings

Identifies key open problems in extending the formalism

Highlights the complexity of transitioning from particle to field ontology

Emphasizes the need for future research to address these challenges

Abstract

We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when one attempts to move from particle ontology into the realm of field ontology, i.e., when one transitions from mechanics to field theory framework. These issues need to be addressed, and problems solved, if one aims to expand the scope of applicability of the process matrix formalism, and therefore its usefulness. This is far from a trivial and straightforward endeavour, but rather a task for a whole future research programme.