Hello, I've reading "Emmy Noether's wanderfull therorem" by Neuenschwander and he asks this question as exersice: We described a transformation that takes us from (t, x) to (t', x') with generators ζ and τ . How would one write the reverse transformation from (t', x') to (t, x) in terms of the original ζ and τ? If the functional is invariant under the ‘forward” transformation, is it also invariant under the “reverse” transformation? I would like to Know whether my answer is correct. For the first question I found that for the inverse tansformation ζ and τ change signs, as for the second question I found that the invariance stands using either the "forward" or "reverse" transformation.