Theorem

Haag's Theorem

Mathematical Physics

Haag's Theorem states that, for a quantum field theory with genuine interaction, the interacting field's representation on Hilbert space cannot be unitarily equivalent to the representation used by the free, noninteracting field, contrary to what the informal interaction-picture formulation of perturbative quantum field theory assumes. Named for Rudolf Haag, it is a foundational rigor result of axiomatic quantum field theory, exposing a mathematical gap between the informal perturbative calculations physicists use and the fully rigorous formulation of the theory.

Facts

Statement

If two Poincaré-invariant quantum fields share the same vacuum, then their first four Wightman functions coincide. 1

Proof Year

1955 1

Classification

Statement Form

Impossibility Theorem 1

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Impossibility Theorem

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Mathematical Physics

Source Haag's theorem (Wikipedia)

Sources

1. Haag's theorem (Wikipedia)

Formal description, second part
If two Poincaré-invariant quantum fields share the same vacuum, then their first four Wightman functions coincide.
Introduction
an argument against the existence of the interaction picture
In Branch: Mathematical Physics, Lead paragraph
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.
In Group: Quantum Mechanics and Quantum Field Theory, Lead section
the mathematical physics of an interacting, relativistic, quantum field theory, Rudolf Haag developed an argument against the

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Haag's Theorem

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