Editing Cluster decomposition (section)

{{Short description|Locality condition in quantum field theory}}
In [[physics]], the '''cluster decomposition property''' states that [[experiment]]s carried out far from each other cannot influence each other. Usually applied to [[quantum field theory]], it requires that [[vacuum expectation value]]s of [[operator (physics)|operators]] localized in [[bounded set|bounded regions]] factorize whenever these regions becomes sufficiently distant from each other. First formulated by [[Eyvind Wichmann]] and James H. Crichton in 1963 in the context of the [[S-matrix|''S''-matrix]],<ref>{{cite journal|last1=Wichmann|first1=E.H.|author-link1=|last2=Crichton|first2=J.H.|author-link2=|date=1963|title=Cluster Decomposition Properties of the S Matrix|url=https://link.aps.org/doi/10.1103/PhysRev.132.2788|journal=Phys. Rev.|volume=132|issue=6|pages=2788–2799|doi=10.1103/PhysRev.132.2788|publisher=American Physical Society|pmid=|arxiv=|bibcode=1963PhRv..132.2788W |s2cid=|access-date=|url-access=subscription}}</ref> it was conjectured by [[Steven Weinberg]] that in the [[effective field theory|low energy limit]] the cluster decomposition property, together with [[Lorentz covariance|Lorentz invariance]] and [[quantum mechanics]], inevitably lead to quantum field theory. [[String theory]] satisfies all three of the conditions and so provides a counter-example against this being true at all energy scales.<ref>{{cite conference|last1=Weinberg|first1=S.|author-link1=|date=1996|title=What is quantum field theory, and what did we think it is?|conference=Conference on Historical Examination and Philosophical Reflections on the Foundations of Quantum Field Theory|url=|journal=|volume=|issue=|pages=241–251|doi=|pmid=|arxiv=hep-th/9702027|s2cid=|access-date=}}</ref>