Hi, i am confused on this question: Wigner proved that a symmetry is represented by either a linear unitary operator or an anti-linear anti-unitary operator. But does it's inverse right? i.e. Does any linear unitary operator stand for a symmetry transformation? It seems to be right, as a unitary operator does not change the inner product of two states, and it holds as time flowing. But this result is too strong to believe, because there are infinity number of linear unitary operators, are there also so many symmetry? Best wishes. Thank you!