Haag's theorem

While working on the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument^[1] 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 Hall & Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields.^[2] A generalization due to Reed & Simon shows that applies to free neutral scalar fields of different masses,^[3] which implies that the interaction picture is always inconsistent, even in the case of a free field.