I'm taking a quantum field theory course and the topic of active vs passive transformations came up. I have previously taken a physics course and active/passive transformations were never explicitly discussed. What is the difference between the two? In particular I'm trying to follow the following argument: Consider a scalar field f(x) which transforms under a Lorentz transformation x->L(x). It transforms as f(x) -> f'(x) = f(L_inverse(x)) Why is it L_inverse(x) instead of L(x)? Thanks.