{"title":"Eliminativism and the QCD \\(\\theta _{\\text {YM}}\\)-Term: What Gauge Transformations Cannot Do","authors":"Henrique Gomes, Aldo Riello","doi":"10.1007/s10701-024-00759-5","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(\\theta _{\\text {YM}}\\)</span>-term to provide a novel argument against the eliminative view. The argument is based on the claim that the QCD <span>\\(\\theta _{\\text {YM}}\\)</span>-term changes under “large” gauge transformations. Here we review geometrical propositions about fiber bundles that unequivocally falsify these claims: the <span>\\(\\theta _{\\text {YM}}\\)</span>-term encodes topological features of the fiber bundle used to represent gauge degrees of freedom, but it is <i>fully</i> gauge-invariant. Nonetheless, within the essentially classical viewpoint pursued here, the physical role of the <span>\\(\\theta _{\\text {YM}}\\)</span>-term shows the physical importance of bundle topology (or superpositions thereof) and thus counts against (a naive) eliminativism.</p></div>","PeriodicalId":569,"journal":{"name":"Foundations of Physics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10701-024-00759-5.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10701-024-00759-5","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
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.