  Haag's theorem has shown that the transformation between interacting and free
field operators in a reasonable quantum field theory cannot be unitary. Here,
the original requirement of unitarity is revisited from a physical point of
view to show not only that unitarity is not required but indeed not possible.
Electrodynamics is used as an example. In a classical treatment the interaction
cannot be turned on or off adiabatically as energy conservation cannot be
maintained in a physically meaningful way. In a fully second quantized theory
the interaction (or source) term is always present in the equation of motion
even if the system is in the vacuum state. So, the interaction cannot be
physically turned on or off adiabatically or otherwise. Hence, the
transformation V(t) from free fields to interacting fields cannot be
interpreted as an actual time evolution. This makes the unitarity of V(t)quite
unnecessary as the original reason for unitarity was to conserve probability
(or energy) through a time evolution. It is conjectured that the infinite terms
in the scattering matrix that need renormalization appear due to the forcing of
V(t)to be unitary. An alternate approach to scattering of interacting fields is
suggested.
