The Lorentz groups act on the scalar fields as: ϕ′(x)=ϕ(Λ−1x)
The conditions for an action of a group on a set are that the identity does nothing and that (g1g2)s=g1(g2s). This second condition is not fulfilled because of the inverse on Λ. What is then the action of the Lorentz group on the scalar fields?
This post imported from StackExchange Physics at 2014-03-22 17:31 (UCT), posted by SE-user inquisitor