I was studying a course about Lie groups, Lie algebras and their representations (and classifications) when I encountered this statement :
When a physical system admits symmetry, the observable form a representation of the group concerned. Lorentz and Poincaré groups are very important examples.
(It's originally in french so this transduction might be a bit off)
This sounds like it's very important to understand the "big picture" of such theories but I don't really understand it. Is this only for quantum theories? If so, what is the link between representation theory and observable?
I'm in first year of master so I can understand concepts about Lie groups, Lie algebras, manifolds, QFT, etc.