Q: What are the asymptotic momentum eigenstates? Dressed quanta or quanta of free theory? Suppose I consider an interacting theory, say QED (with electrons and photons). Let, free electrons, I mean the quanta of the free Dirac Lagrangian. The dressed electron differs from the free electron by a renormalized mass and renormalized charge. 
When we consider scattering, do we consider scattering between free Dirac electrons or renormalized electrons? In other words, I want to understand whether the asymptotic momentum eigenstates in the LSZ formalism, are electrons of the free theory or dressed electrons.

A: Its dressed electrons.
Remember how we are only considering one-particle-irreducible diagrams when evaluating the S-matrix element between two asymptotic states? Well, this is exactly because the asymptotic states are dressed. Intuitively, the diagrams with self-energy corrections are already accounted for because the states are dressed and we have to "amputate the legs" to calculate the amplitude between dressed states.
