I read in a QFT book that local gauge symmetry implies causality. Could someone please explain that statement and why it's true?
Thank you.
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asked Oct 15, 2013 at 14:24
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3$\begingroup$ in which book did you read that? $\endgroup$– innisfreeCommented Oct 15, 2013 at 14:27
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3$\begingroup$ ...indeed that is a bizarre thing to say. As Nima Arkani-Hamed loves to say "any dumb theory is a gauge theory" - gauge invariance is just a redundancy of description. It's only there to get rid of unphysical degrees of freedom you added to make things more convenient. So it can't imply anything truly deep like causality unless there are some other assumptions behind it. If anything the general implication goes the other way, i.e. causality + locality -> only physical degrees of freedom allowed in observables -> gauge invariance of any redundant description. $\endgroup$– MichaelCommented Oct 15, 2013 at 14:38
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$\begingroup$ @MichaelBrown seems to be dicussed in e.g. arxiv.org/abs/1306.5750, though it conludes that gauge symmetry implies causality only for low-spin systems (?) $\endgroup$– innisfreeCommented Oct 15, 2013 at 15:16
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$\begingroup$ @innisfree The book is called Quantum Field Theory - Demystified, at the beginning of the chapter of the Higgs mechanism. The book can be fo with some digging. $\endgroup$– The Quantum PhysicistCommented Oct 15, 2013 at 17:15
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It's just not true that local gauge symmetry implies causality. That's a false statement. And, from what I can tell, the textbook you reference does not make this assertion. It only says that local gauge symmetry preserves causality, meaning that the two concepts are compatible.
