"In a Lorentz invariant theory in d dimensions a state forms an irreducible representation under the subgroups of [itex]SO(1,d-1)[/itex] that leaves its momentum invariant." I want to understand that statement. I don't see how I should interpret a state as representation of a group. I have learned that representations of groups are maps which assign a linear transformation between vector spaces (or matrix) to each group element. But why should a state correspond to such a mapping? I am completely lost here. I would be happy if someone could clear this up for me.