Question

In QFT, how can it be shown that the field out, ${\phi_{out}}$, is a free field if the field in, ${\phi_{in}}$, is a free field?

Answer 1

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics. ... QFT treats particles as excited states of an underlying field, so these are called fieldquanta.

Answer 2

As of now the standard model, described correctly by Quantum Field Theory, has 12 fundamental fields for fermions (6 quarks and 6 leptons) and 12 fundamental fields for bosons (8 gluons, 2 for W and Z bosons, 1 for the photon and 1 for the Higgs boson).