Talk:Gauge group (mathematics)

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Mathematics Mid‑priority

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Is this physics or maths[edit]

This page is titled Gauge group (mathematics) but except for a terse definition of the automorphisms of a principal bundle all the examples seem to be from physics. I suggest a new page called Gauge group (physics) is created which houses that information, and this page becomes a reference for the definition of a gauge transformation in the mathematical literature (both on a principal bundle and vector bundle, and so on), or if these topics don't serve to stand on their own I suggest we rename the page Gauge group and include independent but interlinking mathematical and physics discussions of the concept. I certainly think it is worth having a page on wikipedia that explains clearly the difference in terminology in mathematics and physics of the terms gauge transformation, gauge symmetry, local gauge transformation, local gauge symmetry, and gauge group, which this page attempts but falls short at.

If no one has any objections, I will undertake one of these options at my discretion.Tazerenix (talk) 00:07, 13 June 2020 (UTC)[reply]

Following on from this, could someone who knows more of the physical terminology fill in the blanks/corrections in this correspondence list, and add any extra important terms if you know them!

Differential geometry	Physics
Structure group	Gauge group
Gauge group	Group of (global?) gauge transformations
Gauge transformation	(global?) gauge transformation
Change of local trivialisation	Local gauge transformation
Choice of local trivialisation	Fixing a gauge
Set of gauge transformations that leave a Lagrangian functional defined on the set of connections invariant (?)	Global gauge symmetry
A local change of trivialisation that leaves the local form of a Lagrangian functional defined on the set of connections invariant (?)	Local gauge symmetry
Connection	(Gauge field?) or gauge potential
Curvature	Gauge field strength

Tazerenix (talk) 10:48, 13 June 2020 (UTC)[reply]