Global vs. Local (gauge) Symmetry

  • #1
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.
 

Answers and Replies

  • #2
vanhees71
Science Advisor
Insights Author
Gold Member
2021 Award
19,537
10,296
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
 
  • Like
Likes ohwilleke and paralleltransport

Related Threads on Global vs. Local (gauge) Symmetry

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
14
Views
8K
Replies
2
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
10
Views
6K
Replies
5
Views
1K
  • Last Post
Replies
2
Views
914
  • Last Post
Replies
2
Views
7K
Replies
1
Views
703
Replies
4
Views
1K
Top