I am self studying quantum field theories and as many of you know this can not be properly done without at least some knowledge of Lie groups and the corresponding algebra.
I am reading the QFT text by Michele Maggiore “A modern introduction to quantum field theory”. In his chapter on Lie groups (I know, a single chapter is far from enough) he defines a representation of the Lie group as an operation that assigns a linear operator to each element within the Lie group.
My question is, does all Lie groups has such a (linear) representation? Or is Michele Maggiore restricting his discussion on Lie groups to that of matrix Lie groups without explicitly stating so?
This might be trivial question, but I am new to Lie groups and is just seeking some clarification on the topic.