Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T05:00:04.589Z Has data issue: false hasContentIssue false
  • English
  • Français

Understanding Gauge

Published online by Cambridge University Press:  01 January 2022

James Owen Weatherall
Get access Rights & Permissions [Opens in a new window]

Abstract

I consider two usages of the expression “gauge theory.” On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in which one formulation of electromagnetism, the paradigmatic gauge theory on both usages, may be understood to have excess structure and then argue that gauge theories on the second usage, including Yang-Mills theory and general relativity, do not generally have excess structure in this sense.

Type
Formal Methods
Information
Philosophy of Science , Volume 83 , Issue 5 , December 2016 , pp. 1039 - 1049
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

This material is based on work supported by the National Science Foundation under grant 1331126. Thank you to Thomas Barrett, Gordon Belot, Ben Feintzeig, Richard Healey, David Malament, Sarita Rosenstock, and David Wallace for helpful discussions related to the material in this article; to Thomas Barrett, Ben Feintzeig, David Malament, J. B. Manchak, and Sarita Rosenstock for comments on an earlier draft; and to my fellow symposiasts—Thomas Barrett, Hans Halvorson, and Sahotra Sarkar—for a stimulating session at the 2014 PSA biennial meeting, at which this work was presented.

References

Baez, John, Bartel, Toby, and Dolan, Jim. 2004. “Property, Structure, and Stuff.” Quantum Gravity Seminar, University of California, Riverside. http://math.ucr.edu/home/baez/qg-spring2004/discussion.html.Google Scholar
Barrett, Thomas. 2013. “How to Count Structure.” Philosophy of Physics Workshop, Carnegie Mellon University, September.Google Scholar
Bleecker, David. 1981. Gauge Theory and Variational Principles. Reading, MA: Addison-Wesley. Repr., Dover 2005.Google Scholar
Earman, John. 1989. World Enough and Space-Time. Cambridge, MA: MIT Press.Google Scholar
Earman, John 2004. “Laws, Symmetry, and Symmetry Breaking: Invariance, Conservation Principles, and Objectivity.” Philosophy of Science 71 (5): 1227–41.CrossRefGoogle Scholar
Earman, John, and Norton, John. 1987. “What Price Spacetime Substantivalism? The Hole Story.” British Journal for the Philosophy of Science 38 (4): 515–25.CrossRefGoogle Scholar
Healey, Richard. 2007. Gauging What’s Real: The Conceptual Foundations of Contemporary Gauge Theories. New York: Oxford University Press.CrossRefGoogle Scholar
Ismael, Jenann, and van Fraassen, Bas. 2003. “Symmetry as a Guide to Superfluous Structure.” In Symmetries in Physics: Philosophical Reflections, ed. Brading, Katherine and Castellani, Elena, 371–92. Cambridge: Cambridge University Press.Google Scholar
Leinster, Tom. 2014. Basic Category Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Mac Lane, Saunders. 1998. Categories for the Working Mathematician. 2nd ed. New York: Springer.Google Scholar
Malament, David. 2012. Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Martin, Christopher A. 2002. “Gauge Principles, Gauge Arguments, and the Logic of Nature.” Philosophy of Science 69 (Proceedings): S221–S234.CrossRefGoogle Scholar
Palais, Richard S. 1981. The Geometrization of Physics. Hsinchu: Institute of Mathematics, National Tsing Hua University.Google Scholar
Redhead, Michael. 2003. “The Interpretation of Gauge Symmetry.” In Symmetries in Physics: Philosophical Reflections, ed. Brading, Katherine and Castellani, Elena, 124–39. Cambridge: Cambridge University Press.Google Scholar
Rosenstock, Sarita, Barrett, Thomas, and Weatherall, James Owen. 2015. “On Einstein Algebras and Relativistic Spacetimes.” Studies in History and Philosophy of Modern Physics B 52:309–16.CrossRefGoogle Scholar
Rosenstock, Sarita, and Weatherall, James Owen. 2015. “A Categorical Equivalence between Generalized Holonomy Maps on a Connected Manifold and Principal Connections on Bundles over That Manifold.” Unpublished manuscript, arXiv. http://arxiv.org/abs/1504.02401.Google Scholar
Rovelli, Carlo. 2013. “Why Gauge?” Foundation of Physics 44 (1): 91–104.CrossRefGoogle Scholar
Trautman, Andrzej. 1980. “Fiber Bundles, Gauge Fields, and Gravitation.” In General Relativity and Gravitation, ed. Held, A., 287–308. New York: Plenum.Google Scholar
Wald, Robert. 1984. General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Weatherall, James Owen. 2015. “Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?” Erkenntnis, forthcoming. doi:10.1007/s10670-015-9783-5.CrossRefGoogle Scholar
Weatherall, James Owen 2016a. “Fiber Bundles, Yang-Mills Theory, and General Relativity.” Synthese 193 (8): 2389–2424.CrossRefGoogle Scholar
Weatherall, James Owen 2016b. “Regarding the ‘Hole Argument.’” British Journal for Philosophy of Science, forthcoming. doi:10.1093/bjps/axw012.CrossRefGoogle Scholar
Weyl, Hermann. 1952. Space-Time-Matter. Mineola, NY: Dover.Google Scholar

A correction has been issued for this article:

Erratum