Identical Particles and Statistics in Superselection Theory

超选择理论中的相同粒子和统计

• 批准号: 1127260
• 负责人: David Baker
• 金额: $ 12.5万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1127260&HistoricalAwards=false
• 关键词: Identical; Particles; Statistics; Superselection; Theory

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.

相同的量子粒子（例如费米子和玻色子）具有有趣的统计特性（玻色统计和费米统计），这给天真的哲学解释带来了严重的问题。相同粒子解释研究的主要背景是基础量子力学。 PI 提议在更基础的量子场论背景下开展解释性研究。这项研究涉及由 Doplicher、Haag 和 Roberts 在量子场论的代数表述中发展起来的超选择理论。该理论提供了超选择的数学解释，否则超选择将是一组假设的规则，禁止准备与不同类型的相同粒子相关的状态叠加。他们计划将注意力集中在两个研究问题上。第一个问题涉及超选择理论（在量子场论的代数表述中）是否为系统为什么遵循玻色统计而不是费米统计提供了更基本的解释（例如）。第二个项目讨论了如何根据反对粒子存在的有力论据，在量子场论中理解涉及相同粒子的科学结果。智力价值。该项目将使量子场论哲学与量子力学哲学中长期存在的问题相联系。量子场论一直是许多新概念问题的根源，特别是（尽管不仅仅是）与理论的酉不等价表示的存在有关。这导致了许多富有成效的研究，但也导致量子场论哲学和量子力学工作之间缺乏联系，即使是在量子场论研究应该涉及较早争论的领域也是如此。统计学的形而上学就是这样一个很大程度上被忽视的领域。更广泛的影响这是一个深度跨学科的项目，汇集了哲学、现代物理学和数学的各个方面。它本着这些领域之间合作（而不是批判）交流的精神进行，并将有助于加强科学与科学哲学之间一些关键接触点的建设性发展。该项目的结果将引起数学家、物理学家和科学哲学家的兴趣。该项目还集教学和研究于一体；高级研究员计划就该项目的主题举办研究生研讨会；初级研究员将参与该课程的教学。