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.

全同的量子粒子（如费米子和玻色子）具有有趣的统计性质（玻色统计和费米统计），这给天真的哲学同一性解释带来了严重的问题。全同粒子的解释性研究的主要背景是基础量子力学。PI建议在量子场论的背景下开展解释性研究，这是更基本的。这项研究涉及一个理论的超选择发展的代数公式的量子场论的多普利彻，哈格和罗伯茨。该理论为超选择提供了一个数学解释，否则它将是一组假设的规则，禁止与不同类型的相同粒子相关的态的叠加。他们计划把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）是否为为什么系统服从玻色统计而不是费米统计（例如）提供了更基本的解释。第二个项目是讨论如何在量子场论中理解涉及全同粒子的科学结果，并提出有力的论据来反对粒子的存在。智力成果。该项目将使量子场论的哲学与量子力学哲学中长期存在的问题联系起来。量子场论是许多新概念问题的来源，特别是（但不仅仅是）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接触，即使在量子场论研究应该与旧争论有关的领域。统计学的形而上学就是这样一个被广泛忽视的领域。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。它本着这些领域之间的合作（而不是批判）交流的精神进行，它将有助于加强科学与科学哲学之间某些关键联系点的建设性发展。这个项目的结果将被证明是感兴趣的数学家，物理学家和科学哲学家。该项目还将教学和研究相结合;高级研究员计划就项目主题讲授研究生研讨会;初级研究员将参与讲授课程。