Why is ##\bar{\psi}=e^{i\theta}\psi##, where ##\theta## is a real number, used as the global gauge transformation? Why ##e^{i \theta}##; what's the physical significance or benefit?(adsbygoogle = window.adsbygoogle || []).push({});

Why is ##\bar{\psi} = e^{i \theta(x)} \psi## the local gauge transformation? What does ##\theta## being a function of ##x## instead of a real number change such that it no longer applies globally?

Thank you in advance for any explanations. I'm sorry if my questions are trivial!

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# ##\bar{\psi}=e^{i\theta}\psi## global gauge transformation

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