The causal axioms of algebraic quantum field theory: A diagnostic

IF 1.4 2区 哲学 Q1 HISTORY & PHILOSOPHY OF SCIENCE Studies in History and Philosophy of Science Pub Date : 2024-03-18 DOI:10.1016/j.shpsa.2024.01.006
Francisco Calderón
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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.

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代数量子场论的因果公理:诊断
代数量子场论(AQFT)提出了三个 "因果公理",旨在将该理论描述为实现相对论因果关系的理论:频谱条件、微因果性和原始因果性。在本文中,我的目的是用最简单的技术方法来说明,它们都不能完全解释适合于 AQFT 的因果概念,因为它们只捕捉到了我所说的相对论因果性的一些必要条件,或者说,因为每个公理如何实现各自的必要条件往往并不清楚。在诊断之后,我将证明第四个条件--局部原始因果性(LPC)--在满足所有相关必要条件的意义上完全描述了相对论因果性。然而,正如我将从哈格和施罗尔(1962 年)的构造中说明的那样,它只是包含了其他公理的优点,因为它是由这些公理所隐含的。由于三个因果公理的结合意味着 LPC 以及 LPC 并不意味着的 QFT 中的其他重要结果,并且由于 LPC 有助于澄清三个公理的一些缺陷,因此我主张对公理如何表征 AQFT 因果结构进行整体解释,以反对文献中将公理对立起来并优先考虑其中一个公理的策略。
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来源期刊
Studies in History and Philosophy of Science
Studies in History and Philosophy of Science 管理科学-科学史与科学哲学
CiteScore
2.50
自引率
10.00%
发文量
166
审稿时长
6.6 weeks
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.
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