Cluster decomposition

<p>In <a href="/facts/Physics/a7aH2y08">physics</a>, the cluster decomposition property states that <a href="/facts/Experiment/esltM54f">experiments</a> carried out far from each other cannot influence each other. Usually applied to <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, it requires that <a href="/facts/Vacuum_expectation_value/117KpmVM">vacuum expectation values</a> of <a href="/facts/Operator_(physics)/rCJw8UFz">operators</a> localized in <a href="/facts/Bounded_set/yCldjtoy">bounded regions</a> factorize whenever these regions becomes sufficiently distant from each other. First formulated by <a href="/facts/Eyvind_Wichmann/JkJ7YEEb">Eyvind Wichmann</a> and James H. Crichton in 1963 in the context of the <a href="/facts/S-matrix/NffJvlpp"><i>S</i>-matrix</a>, it was conjectured by <a href="/facts/Steven_Weinberg/G61D6kJw">Steven Weinberg</a> that in the <a href="/facts/Effective_field_theory/oQ2nWoko">low energy limit</a> the cluster decomposition property, together with <a href="/facts/Lorentz_covariance/K5AEuGKg">Lorentz invariance</a> and <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, inevitably lead to quantum field theory. <a href="/facts/String_theory/HUJFIPYH">String theory</a> satisfies all three of the conditions and so provides a counter-example against this being true at all energy scales.
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Cluster decomposition open-in-new

Cluster decomposition