Simulating Nelsonian Quantum Field Theory

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY Foundations of Physics Pub Date : 2024-05-15 DOI:10.1007/s10701-024-00766-6
Andrea Carosso
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Abstract

We describe the picture of physical processes suggested by Edward Nelson’s stochastic mechanics when generalized to quantum field theory regularized on a lattice, after an introductory review of his theory applied to the hydrogen atom. By performing numerical simulations of the relevant stochastic processes, we observe that Nelson’s theory provides a means of generating typical field configurations for any given quantum state. In particular, an intuitive picture is given of the field “beable”—to use a phrase of John Stewart Bell—corresponding to the Fock vacuum, and an explanation is suggested for how particle-like features can be exhibited by excited states. We then argue that the picture looks qualitatively similar when generalized to interacting scalar field theory. Lastly, we compare the Nelsonian framework to various other proposed ontologies for QFT, and remark upon their relative merits in light of the effective field theory paradigm. Links to animations of the corresponding beables are provided throughout.

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模拟纳尔逊量子场论
在对爱德华-纳尔逊应用于氢原子的理论进行介绍性回顾之后,我们描述了爱德华-纳尔逊的随机力学在归纳为在晶格上正则化的量子场论时所提出的物理过程图景。通过对相关随机过程进行数值模拟,我们发现纳尔逊理论为任何给定量子态提供了生成典型场配置的方法。特别是,我们给出了与福克真空相对应的场 "beable"--用约翰-斯图尔特-贝尔(John Stewart Bell)的话来说--的直观图景,并对激发态如何表现出类似粒子的特征提出了解释。然后,我们论证了将这幅图景泛化到相互作用标量场理论时,它在质量上看起来是相似的。最后,我们将纳尔逊框架与其他各种为 QFT 提出的本体论进行了比较,并根据有效场论范式评论了它们的相对优点。我们还提供了相应的动画链接。
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来源期刊
Foundations of Physics
Foundations of Physics 物理-物理:综合
CiteScore
2.70
自引率
6.70%
发文量
104
审稿时长
6-12 weeks
期刊介绍: The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.
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