# Global vs. Local (gauge) Symmetry

Summary:
Let's pick a good definition of gauge "symmetry"
Gauge symmetry is highly confusing, partly because many definitions differ in the literature. Strictly speaking gauge symmetry should be called gauge redundancy since you are mapping multiple representations to the same physical state.

What is your favourite definition of what "large" gauge vs. "smaller" gauge transformations are?
What subtle points do you know about the distinction between a global vs. a local gauge transformation is (any examples)?

I'm polling because I have seen conflicting definitions in the literature.

vanhees71

vanhees71
Gold Member
2021 Award
I'd never call a global symmetry gauge symmetry, because that's indeed confusing. A gauge "symmetry" is indeed exactly defined as you write in your first paragraph, and to call it "gauge redundancy" would be a much more accurate choice of terminology (it implies also that local gauge symmetries cannot be spontaneously broken, which is known as Elitzur's theorem; it's rather the "Higgs mechanism" than spontaneous symmetry breaking).

A very nice and pedagogical paper on these issues the following in connection with superconductivity and electromagnetic gauge symmetry:

https://arxiv.org/abs/cond-mat/0503400
https://doi.org/10.1016/j.aop.2005.03.008

ohwilleke and paralleltransport