Editing Haag's theorem (section)

{{Short description|Theorem which describes the interaction picture as incompatible with relativistic quantum fields}}
{{use dmy dates|date=February 2021}}
While working on the [[mathematical physics]] of an interacting, [[Special Relativity|relativistic]], [[quantum field theory]], [[Rudolf Haag]] developed an argument<ref>{{cite journal |last=Haag |first=Rudolf |author-link=Rudolf Haag |year=1955 |title=On quantum field theories |url=http://cdsweb.cern.ch/record/212242/files/p1.pdf |journal=Matematisk-fysiske Meddelelser |volume=29 |page=12}}</ref> 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.<ref>{{cite journal |last1=Hall |first1=Dick  |last2=Wightman |first2=A.S. |author2-link=Arthur Wightman |year=1957 |title=A theorem on invariant analytic functions with applications to relativistic quantum field theory |url=http://gymarkiv.sdu.dk/MFM/kdvs/mfm%2030-39/mfm-31-5.pdf |journal=Matematisk-fysiske Meddelelser |volume=31 |number=5}}</ref> A generalization due to [[Michael C. Reed]] and [[Barry Simon]] shows that applies to free neutral [[scalar field]]s of different masses,<ref>{{cite book |last1=Reed |first1=Michael C. |author1-link=Michael C. Reed |last2=Simon |first2=Barry |author2-link=Barry Simon |series=Methods of Modern Mathematical Physics |volume=II |year=1975 |title=Fourier analysis, self-adjointness |publisher=Academic Press |place=New York, NY |at=Theorem&nbsp;X.46}}</ref> which implies that the interaction picture is always inconsistent, even in the case of a free field.