The Causal Axioms of Algebraic Quantum Field Theory: A Diagnostic
Abstract
Algebraic quantum field theory (AQFT) puts forward three "causal axioms" that aim to characterize the theory as one that implements relativistic causation: the spectrum condition, microcausality, and primitive causality. In this paper, I aim to show, in a minimally technical way, that none of them fully explains the notion of causation appropriate for AQFT because they only capture some of the desiderata for relativistic causation I state or because it is often unclear how each axiom implements its respective desideratum. After this diagnostic, I will show that a fourth condition, local primitive causality (LPC), fully characterizes relativistic causation in the sense of fulfilling all the relevant desiderata. However, it only encompasses the virtues of the other axioms because it is implied by them, as I will show from a construction by Haag and Schroer (1962). Since the conjunction of the three causal axioms implies LPC and other important results in QFT that LPC does not imply, and since LPC helps clarify some of the shortcomings of the three axioms, I advocate for a holistic interpretation of how the axioms characterize the causal structure of AQFT against the strategy in the literature to rivalize the axioms and privilege one among them.
 Publication:

arXiv eprints
 Pub Date:
 January 2024
 DOI:
 10.48550/arXiv.2401.06504
 arXiv:
 arXiv:2401.06504
 Bibcode:
 2024arXiv240106504C
 Keywords:

 Mathematical Physics;
 Physics  History and Philosophy of Physics;
 Quantum Physics
 EPrint:
 Forthcoming in Studies in History and Philosophy of Science