{"title":"The causal axioms of algebraic quantum field theory: A diagnostic","authors":"Francisco Calderón","doi":"10.1016/j.shpsa.2024.01.006","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>Haag and Schroer (1962)</span>. 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.</p></div>","PeriodicalId":49467,"journal":{"name":"Studies in History and Philosophy of Science","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in History and Philosophy of Science","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0039368124000268","RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Studies in History and Philosophy of Science is devoted to the integrated study of the history, philosophy and sociology of the sciences. The editors encourage contributions both in the long-established areas of the history of the sciences and the philosophy of the sciences and in the topical areas of historiography of the sciences, the sciences in relation to gender, culture and society and the sciences in relation to arts. The Journal is international in scope and content and publishes papers from a wide range of countries and cultural traditions.