4
votes
2answers
174 views

Is there a general relationship between the conformal weight of a field and its (classical) scaling dimension?

A field $\phi(z)$ has the conformal weight $h$, if it transforms under $z\rightarrow z_1(z)$ as $$ \phi(z) = \tilde{\phi}(z_1)\left(\frac{dz_1}{dz}\right)^h $$ The (classical) scaling dimension can ...
6
votes
2answers
447 views

Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...