Haag's theorem

While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the existence of the interaction picture, a result now commonly known as Haag's theorem. Haag's original proof relied on the specific form of then-common field theories, but subsequently generalized by a number of authors, notably Dick Hall and Arthur Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields. A generalization due to Michael C. Reed and Barry Simon shows that applies to free neutral scalar fields of different masses, which implies that the interaction picture is always inconsistent, even in the case of a free field.