Symmetries and Conversation Laws

[jensa]

Thanks genneth. Your reply has been very interesting. You have definitely raised my interest for Wen's book, which I have so far only read parts of.

 

[humanino]

There is no stupid question and it's very good to ask about fundamentals
I don't think it's strictly fair to say that's simply relativity, because absolute phase is not an observable. So we're playing around with the concepts, that's true, but enforcing self consistency.

 

[genneth]

Just to add to my entirely incoherent ramblings: there may be a very good reason for favouring gauge field theories (in the sense of having a configuration space that consists of a connection) over other multi-labelled systems. Mass terms are deadly for the naturalness of a field theory with small couplings; any mass term would grow very fast with renormalisation (in the Kadanoff-Wilson sense), and naturally all masses at low energy would be on the order of the theory's UV cutoff. Gauge field theories are protected by symmetry, so produced vector bosons which are guaranteed to be massless.

Open question: does this picture hold for theories which are not weakly coupled? The key question is what the scaling dimension of various local operators actually are, near whichever fixed point the theory actually flows to.