Editing Haag's theorem (section)

== Physical / heuristic point of view ==
As was already noticed by [[Rudolf Haag|Haag]] in his original work, [[vacuum polarization]] lies at the core of Haag's theorem. Any interacting quantum field (or non-interacting fields of different masses) polarizes the vacuum, and as a consequence the vacuum state lies inside a renormalized Hilbert space <math>\;H_\text{renorm}\;</math> that differs from the Hilbert space <math>\;H_\text{free}\;</math> of the free field. Although an [[isomorphism]] could always be found that maps one Hilbert space into the other, Haag's theorem implies that no such mapping could deliver unitarily equivalent representations of the corresponding [[canonical commutation relations]], i.e. unambiguous physical results.