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As a disclaimer, the only gauge theory I know so far is from electromagnetism.

I have read that gauge theory is a big part of modern physics and it heavily underlies much of the standard model. However, what I have not yet learned is how does the concept of a gauge itself lead to new insights about physics? So far it seems to be mostly a mathematical trick that helps make certain calculations easier.

CBBAM
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    related/required reading: https://physics.stackexchange.com/q/13870/50583, https://physics.stackexchange.com/q/370770/50583, https://physics.stackexchange.com/q/76477/50583 and some of their linked questions – ACuriousMind Feb 11 '23 at 19:10
  • If you want to encode a massless spin one particle into a vector field you need gauge invariance. Likewise if you want to encode a massless spin two particle in an tensor that behaves like the metric you need gauge invariance. See Weinberg's TQTF Chapter 5. – Gold Feb 11 '23 at 19:29

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