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
StatementIf two Poincare-invariant quantum fields share the same vacuum, then their first four Wightman functions coincide. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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
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