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- TL;DR Summary
- Lawrence Krauss states that the connection term in EM gauge symmetry is the EM field and that it "... allows us to change our definition of electric charge from place to place." I don't see what it has to do with changing the definition (+ or -) of electric charge.

Lawrence Krauss, "The greatest story ever told ... so far", pp. 108-109. "Gauge symmetry in electromagnetism says that I can actually change my definition of what a positive charge is locally at each point of space without changing the fundamental laws associated with electric charge, as long as I also somehow introduce some quantity that helps keep track of this change of definition from point to point. This quantity turns out to be the electromagnetic field."

Introductions, like Robinson or Schwichtenberg, talk only about local U(1) without making it clear just what the U(1) transformation is changing. Sure, it's the field, but claiming that that

What have I missed?

Introductions, like Robinson or Schwichtenberg, talk only about local U(1) without making it clear just what the U(1) transformation is changing. Sure, it's the field, but claiming that that

*is*the charge escapes me.What have I missed?