I'm starting to learn about particle physics but I really want to see the whole picture before going deep. Here is what I know: - There are symmetries in quantum physics, which are symmetry operators commute with the Hamiltonian (translation operators, rotation operators...) which act on a physics state. (I think these operators form groups) - The representation theory: each particle corresponds to a representation (in the simplest meaning) I want to ask is there any relation between the groups of opertors in the first and the groups belonging to representation in the second? Thank you and I'm sorry if I'm being naive. I'm really not knowing anything about this field. I'm just trying to picturize.