代数量子场论的因果公理：一项诊断
The Causal Axioms of Algebraic Quantum Field Theory: A Diagnostic
AI总结：
本文诊断了AQFT的三个因果公理未能充分刻画相对论因果性，并论证局部原始因果性（LPC）虽能完全满足必要条件，但应整体性理解公理体系，而非在它们之间择一优先。
摘要：
代数量子场论（AQFT）提出了三个“因果公理”，旨在将该理论刻画为实现相对论因果性的理论：谱条件、微观因果性和原始因果性。在本文中，我旨在以最少技术性的方式表明，这些公理均未完全解释适用于AQFT的因果性概念，因为它们仅捕获了我所陈述的关于相对论因果性的部分必要条件，或者因为每个公理如何实现其各自的必要条件常常不清楚。经过这一诊断后，我将表明，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，完全刻画了相对论因果性。然而，它仅包含其他公理的优点，因为它由它们蕴含，正如我将从Haag和Schroer（1962）的一个构造中所示。由于三个因果公理的合取蕴含LPC以及QFT中其他LPC不蕴含的重要结果，并且由于LPC有助于澄清三个公理的一些缺点，我主张对公理如何刻画AQFT的因果结构进行整体性解释，反对文献中将公理对立化并特权的策略。
英文摘要：
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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