The Role of the Classical Limit and Symmetries in Constructing Quantum Theories

这是一个关于物理学哲学基础的研究项目。研究小组将研究构建量子理论的技术和哲学方面的问题，包括经典理论的量子化过程和与之密切相关的经典极限取值过程；他们将关注对称性在这些过程中的作用。这部分研究的结果将用于发展关于理论构建、科学进步和解释的概念和哲学问题的新见解。为了实现这些目标，该团队将开发概念和数学工具，他们期望这些工具将为物理学指明新的方向，也许会为解决数学物理中的一些开放问题提供建议。研究人员将通过举办两场研讨会来建立一个新的跨学科研究社区，以促进物理学哲学家和当代物理学家之间的进一步对话。他们还将利用项目中的技术来解释量子理论，从而在本科阶段创造新的教学方法。研究团队将聚焦于物理学理论建构的一个重要特征，即对称性的使用，对量子化过程的哲学意义进行个案研究。他们将讨论几个相互关联的问题。为什么对称性在量子理论的构建中如此有用？量子理论中的对称性与经典理论中的对称性有什么关系？对称性如何限制新理论的构建？在解决这些问题时，他们将专注于粒子在外部规范场中运动的理论；这样的理论具有有限的自由度，这意味着它们在数学上是易于处理的。目标将是构建数学工具，使人们能够比较经典物理学和量子物理学的模型和理论。然后，该团队将调查他们关于从经典理论到量子理论过渡的见解如何与科学哲学中的一般问题相关。他们将在项目的这个阶段考虑几个问题。经典物理学和量子物理学之间的过渡在多大程度上可以被理解为连续的和累积的？我们能精确地描述在经典描述和量子描述之间变化的表征结构吗？量子理论的构建必须通过构建单个模型来分段完成，还是有可能整体构建理论框架？该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This is a research project in the philosophical foundations of physics. The research team will investigate technical and philosophical aspects of constructing quantum theories, including the process of quantizing classical theories and the closely related process of taking the classical limit; they will focus on the role of symmetries in these processes. The results of this part of the study will then be used to develop new insights concerning both conceptual and philosophical issues surrounding theory construction, scientific progress, and explanation. In addressing these goals, the team will develop conceptual and mathematical tools that they expect will indicate new directions for physics, perhaps leading to recommendations for solving some open problems in mathematical physics. The researchers will build a new interdisciplinary research community by hosting two workshops to facilitate further conversations between philosophers of physics and contemporary physicists. They will also create new teaching methods at the undergraduate level by using techniques from the project for interpreting quantum theories. The research team will focus on the role of one important feature of theory construction in physics, the use of symmetries, to develop a case study of the philosophical significance of quantization procedures. They will address several interrelated questions. Why are symmetries so useful in the construction of quantum theories? How are symmetries in quantum theories related to symmetries in classical theories? How do symmetries constrain the construction of new theories? In addressing these questions, they will focus on theories of particles moving in an external gauge field; such theories have finitely many degrees of freedom, meaning that they are mathematically tractable. The goal will be to construct mathematical tools that allow one to compare models and theories across classical and quantum physics. The team will then investigate how their insights about transitions from classical to quantum theories relate to general issues in philosophy of science. They will consider several questions in this phase of the project. To what extent can the transition between classical and quantum physics be understood as continuous and cumulative? Can one make precise the representational structure that changes between classical and quantum descriptions? Must the construction of quantum theories be done piecewise by constructing individual models, or is it possible to construct the theoretical framework wholesale?This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.