- #1
dfttheory
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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 (\psi \rightarrow e^{i \theta (x)} \psi) 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!
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!
