- #1
unchained1978
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I'm currently working through Griffith's book Introduction to Elementary Particles, and studying the chapters on gauge theories. From classical E&M, I understand what we mean by a gauge transformation and why the Lagrangian must be invariant under such a transformation, but what I don't understand is what a phase transformation of the form [itex]\psi\to e^{i\theta(x)}\psi[/itex] represents and how the gauge field [itex]A_{\mu}[/itex] necessarily arises from such a transformation. It seems like this is a potentially deep connection between rotating the fields [itex]\psi[/itex] and introducing a vector potential, but I don't understand what is actually going on when we apply a phase transformation. If anyone could elaborate or provide some intuition for what a phase transformation really is I would greatly appreciate it.