Identical Particles and Statistics in Superselection Theory

相同的量子粒子（如费米子和玻色子）具有有趣的统计特性（玻色统计和费米统计），这对朴素的同一性哲学解释提出了严重的问题。对相同粒子进行解释性研究的主要背景是基本的量子力学。pi建议在量子场论的背景下进行解释性研究，这是更基本的。这项研究涉及到由多普里切、哈格和罗伯茨在量子场论的代数表述中发展出来的超选择理论。该理论为超选择提供了一种数学解释，否则这将是一套假定的规则，禁止准备与不同类型的相同粒子相关的叠加态。他们计划将注意力集中在两个研究问题上。第一个问题是超选择理论（在量子场论的代数表述中）是否提供了一个更基本的解释，来解释为什么系统服从玻色而不是费米统计（例如）。第二章论述了在反对粒子存在的有力论据中，如何在量子场论中理解涉及相同粒子的科学结果。知识价值。这个项目将把量子场论哲学与量子力学哲学中长期存在的问题联系起来。量子场论已经成为许多新概念问题的来源，特别是（尽管不是唯一的）与理论的幺正不等价表示的存在有关。这导致了许多卓有成效的研究，但也导致了量子场论哲学与量子力学工作之间缺乏接触，即使在量子场论研究应该与旧辩论有关的领域也是如此。统计学的形而上学就是这样一个在很大程度上被忽视的领域。更广泛的影响这是一个深入的跨学科项目，汇集了哲学、现代物理学和数学的各个方面。它在这些领域之间本着合作性（而不是批判性）交流的精神进行，并将有助于在科学与科学哲学之间的一些关键接触点上促进建设性的发展。这个项目的结果将会引起数学家、物理学家和科学哲学家的兴趣。教学与科研相结合；高级研究员计划就该项目的主题教授研究生研讨会；初级研究员将参与课程教学。

Identical quantum particles (such as Fermions and Bosons) have intriguing statistical properties (Bose statistics and Fermi statistics) that raise serious issues for naive philosophical accounts of identity. The predominant context for interpretive studies of identical particles has been basic quantum mechanics. The PIs propose to develop an interpretive study in the context of quantum field theory, which is more fundamental. The study involves a theory of superselection developed in the algebraic formulation of quantum field theory by Doplicher, Haag, and Roberts. The theory provides a mathematical explaination of superselection, which would otherwise be a postulated set of rules that forbid the preparation of a superposition of states associated with different types of identical particles. They plan to focus attention on two research questions. The first concerns whether superselection theory (in the algebraic formulation of quantum field theory) provides a more fundamental explanation for why systems obey Bose rather than Fermi statistics (for example). The second addresses how scientific results involving identical particles are to be understood in quantum field theory, in light of powerful arguments against the existence of particles.Intellectual Merit.This project will bring the philosophy of quantum field theory into contact with long-standing problems in the philosophy of quantum mechanics. Quantum field theory has been the source of many novel conceptual problems, particularly (though not solely) having to do with the existence of unitarily inequivalent representations of the theory. This has led to much fruitful research, but also to a lack of engagement between philosophy of quantum field theory and work on quantum mechanics, even in areas where the study of quantum field theory should bear on the older debates. The metaphysics of statistics is one such largely-neglected area.Broader ImpactsThis is a deeply interdisciplinary project that brings together aspects of philosophy, modern physics, and mathematics. It proceeds in a spirit of cooperative (rather than critical) exchange between these fields, and it will contribute to enhancing constructive developments at some crucial points of contact between science and philosophy of science. The results of this project will prove to be of interest to mathematicians, physicists, and philosophers of science. The project also integrates teaching and research; the senior researcher plans to teach a graduate seminar on the subject matter of the project; the junior researcher will participate in teaching the course.