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Ceci n'est pas un gluon

India Bhalla-Ladd, Eleanor March, James Owen Weatherall

Abstract

We discuss and then resolve a tension between how physicists treat gauge bosons and the celebrated "Wu-Yang dictionary", which identifies particle physics terminology with that of principal bundles and principal connections. We show how this tension leads to an interpretative choice that is not widely discussed in the physics literature. We then show how the same considerations present a dilemma for a recent "particle-first" approach to Yang-Mills theory due to Henrique Gomes. Either the particle-first approach has surplus structure as compared to principal-bundle-based approaches, or gauge bosons are not sections of vector bundles.

Ceci n'est pas un gluon

Abstract

We discuss and then resolve a tension between how physicists treat gauge bosons and the celebrated "Wu-Yang dictionary", which identifies particle physics terminology with that of principal bundles and principal connections. We show how this tension leads to an interpretative choice that is not widely discussed in the physics literature. We then show how the same considerations present a dilemma for a recent "particle-first" approach to Yang-Mills theory due to Henrique Gomes. Either the particle-first approach has surplus structure as compared to principal-bundle-based approaches, or gauge bosons are not sections of vector bundles.
Paper Structure (8 sections, 2 equations, 1 figure)

This paper contains 8 sections, 2 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries: Lie groups, principal bundles, and all that
  3. What is a Gluon?
  4. The textbook account
  5. The Wu-Yang Fictionary?
  6. The resolution, and an interpretive choice
  7. Gomesification
  8. Conclusion

Figures (1)

  • Figure 1: Translation table from the original Wu-Yang dictionary.