Eliminativism and the QCD \(\theta _{\text {YM}}\)-Term: What Gauge Transformations Cannot Do

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY Foundations of Physics Pub Date : 2024-04-24 DOI:10.1007/s10701-024-00759-5
Henrique Gomes, Aldo Riello
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Abstract

The eliminative view of gauge degrees of freedom—the view that they arise solely from descriptive redundancy and are therefore eliminable from the theory—is a lively topic of debate in the philosophy of physics. Recent work attempts to leverage properties of the QCD \(\theta _{\text {YM}}\)-term to provide a novel argument against the eliminative view. The argument is based on the claim that the QCD \(\theta _{\text {YM}}\)-term changes under “large” gauge transformations. Here we review geometrical propositions about fiber bundles that unequivocally falsify these claims: the \(\theta _{\text {YM}}\)-term encodes topological features of the fiber bundle used to represent gauge degrees of freedom, but it is fully gauge-invariant. Nonetheless, within the essentially classical viewpoint pursued here, the physical role of the \(\theta _{\text {YM}}\)-term shows the physical importance of bundle topology (or superpositions thereof) and thus counts against (a naive) eliminativism.

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消除主义与 QCD $$\theta _{\text {YM}}$-Term:量子变换无法做到的事情
关于规规自由度的消解观点--即它们完全源于描述性冗余,因此可以从理论中消解--是物理学哲学中一个生动的辩论话题。最近的工作试图利用QCD \(\theta _{\text {YM}}\)项的性质来提供一个新颖的论据来反对消除性观点。这个论证基于这样一个主张:QCD 的(\theta _{\text {YM}})项在 "大 "规规变换下会发生变化。在这里,我们回顾了关于纤维束的几何命题,这些命题明确地证伪了这些说法:\(\theta _{\text {YM}}\)项编码了用于表示规整自由度的纤维束的拓扑特征,但它是完全规整不变的。尽管如此,在这里所追求的本质上是经典的观点中,\(\theta _{\text {YM}}\)项的物理作用显示了纤维束拓扑学(或其叠加)的物理重要性,因此反对(天真的)消除主义。
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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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