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 Dick Hall and Arthur Wightman, who concluded that no single, universal Hilbert space representation can describe both free and interacting fields.[2] A generalization due to Michael C. Reed and Barry 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.

  1. ^ Haag, Rudolf (1955). "On quantum field theories" (PDF). Matematisk-fysiske Meddelelser. 29: 12.
  2. ^ Hall, Dick; Wightman, A.S. (1957). "A theorem on invariant analytic functions with applications to relativistic quantum field theory" (PDF). Matematisk-fysiske Meddelelser. 31 (5).
  3. ^ Reed, Michael C.; Simon, Barry (1975). Fourier analysis, self-adjointness. Methods of Modern Mathematical Physics. Vol. II. New York, NY: Academic Press. Theorem X.46.