# Fiber bundles, Yang–Mills theory, and general relativity

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## Abstract

I articulate and discuss a geometrical interpretation of Yang–Mills theory. Analogies and disanalogies between Yang–Mills theory and general relativity are also considered.

## Keywords

Yang–Mills theory General relativity Fiber bundle interpretation Holonomy interpretation## Notes

### Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. 1331126. Special thanks are due to participants in my 2012 seminar on Gauge Theories, and especially Ben Feintzeig and Sarita Rosenstock for their many discussions on these topics. I am also particularly indebted to Dick Palais and Bob Geroch for enlightening correspondences on the geometrical foundations of Yang–Mills theory. Helpful conversations and correspondence with Dave Baker, Jeff Barrett, Gordon Belot, Erik Curiel, Katherine Brading, Richard Healey, David Malament, Oliver Pooley, Chris Smeenk, Bob Wald, David Wallace, and Chris Wüthrich have also contributed to the development of the ideas presented here. Erik Curiel, Sam Fletcher, and David Malament read the manuscript carefully and noted several slips (though remaining errors are, of course, my own!). Versions of this paper were presented to the Southern California Philosophy of Physics Group and at the Munich Center for Mathematical Philosophy; I am grateful to the participants there for discussion and comments.

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