We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes in a Hilbert space H. The identities incorporate random shifts of such processes and general Levy measures and seem to be new even for H=R. We illustrate our results showing how the celebrated Dynkin's Isomorphism Theorem follows from such identities. Recall that the Dynkin Isomorphism Theorem relates local times of strongly symmetric Markov processes to Gaussian processes. For another application we consider Levy processes and show how some classical results can simply be derived from isomorphism identities.