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U(1) Gauge symmetry

by dfttheory
Tags: gauge, symmetry, symmetry group, u(1)
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dfttheory
#1
Nov8-13, 11:52 PM
P: 2
So, I have a basic/general question here. I understand that, for example, the QED Langrangian has U(1) gauge symmetry. I also understand that this means (when you have written the Lagrangian with the covariant derivative) that if you transform the wavefunction ([itex]\psi \rightarrow e^{i \theta (x)} \psi[/itex]) and the covariant derivative, this Lagrangian remains invariant.

What I don't understand is this: what does it mean for the wavefunction to have this local symmetry? How do we know that electrons / photons are described by this theory? What principal of nature says that the wavefunction has this symmetry?

I know this is three questions, but I am just trying to get a sense of what informs the choice of symmetry in these theories before I continue transforming and writing gauge invariant theories.

Thank you for any attention you may pay this question!
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dfttheory
#2
Nov8-13, 11:58 PM
P: 2
I just realized that the discussions related to this may contain some of what I am looking for. I would be interested in any additional discussion about this. Thanks!


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