I started reading a document by Gerard 't Hooft which can be found here. Right at the start I am puzzled by a simple expression. It is equation 2.2 showing how a scalar function transforms. I repeat the equation here: $$ \phi^\prime(x) = \phi(x^\prime). \tag{2.2} $$ This does not look right to me. I would expect this to read like: $$ \phi^\prime(x^\prime) = \phi(x). $$ Am I missing something trivial or is this a typo?

  • $\begingroup$ There are tons of differing conventions for this kind of thing -- everybody sets it up their own way. It gets worse -- for the transformation of the action there are fifteen possible conventions, which I outlined here. $\endgroup$ – knzhou Jan 12 at 21:19
  • $\begingroup$ In my opinion the best thing to do is to try to set it all up yourself, in a way that works for you (i.e. so that your calculations get correct results), then basically ignore whatever anybody else does. You can only learn physics by reinventing it, anyway. $\endgroup$ – knzhou Jan 12 at 21:20
  • $\begingroup$ @knzhou-- thanks for the link and comments. Yes this is a confusing bag of notation. I think I need to study also active versus passive transformations. Actually never heard of that before. $\endgroup$ – K7PEH Jan 12 at 21:25
  • $\begingroup$ OK, after a brief look at active and passive transformations I guess I do know what these are -- just didn't know they had a name. $\endgroup$ – K7PEH Jan 12 at 21:27
  • $\begingroup$ Yeah. God knows if that's what t'Hooft had in mind. He could also have just swapped the usual meanings of $x$ and $x'$. There are no universal conventions on this. A more 'casual' document like the one you linked just wouldn't be careful to be consistent on this either. $\endgroup$ – knzhou Jan 12 at 21:30

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