Axiomatic quantum field theory | Theorems in quantum mechanics

Cluster decomposition

In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum expectation values of operators localized in bounded regions factorize whenever these regions becomes sufficiently distant from each other. First formulated by Eyvind H. Wichmann and James H. Crichton in 1963 in the context of the S-matrix, it was conjectured by Steven Weinberg that in the low energy limit the cluster decomposition property, together with 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. (Wikipedia).

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Related pages

Effective field theory | Translational symmetry | Connectivity (graph theory) | String theory | Scattering amplitude | Operator (physics) | Experiment | Constructive quantum field theory | Euler characteristic | S-matrix | Principle of locality | Wightman axioms | Faster-than-light | Conformal field theory | Bounded set | Vertex (graph theory) | Axiomatic quantum field theory | Lorentz covariance | Axiom | Correlation function (quantum field theory) | Fourier transform