Hi! This is my first post.
Do you mean "propagators are Unitary"? I think a propagator is an operator which governs time evolution of an eigenstate. In order that total of probability obtained from the integration of the eigenstate's inner product remains 1 in the course of time evolution, time evolution operator should be Unitary. If so, I think propagators are Green's function used to solve a problem by perturbation method. So although a time evolution operator of an exact solution of the problem should be Unitary, propagators are not neccesarily Unitary, I think. Propagators are not the operators which should be diagonalized by eigenfunctions in order to solve the problem. I heard that S matrix which is constructed by a propagator is Unitary, though. How do you think about this.
Thank you! jeff. Propagators are not operators. However, I found that Feynman propagator was defined by an expectation value in vaccum of two time ordered field operators in quantum field theory. Is this what you mean?