Time as self-adjoint operator?
It has been asked if there exists an operator representing time. I remember some negative answers, but I do not remember the arguments.
In relativistic QM this relates to the non-existence of position operators; we are working with an (t,x,1,x2,x3) vector there. Also I believe to remember some provlem with velocity operators -its eigenvectors been only +c and -c, or so- but I am unsure about if both questions are related.
also, Energy-time indetermination is usedto estimate decay rates of particles. But there an operator is not invoked.