Correlation function: Difference between revisions

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Probability distributions defined on a finite number of points can always be normalized, but when these are defined over continuous spaces, then extra care is called for. The study of such distributions started with the study of [[random walk]]s and led to the notion of the [[Itō calculus]].

The Feynman [[path integral formulation|path integral]] in Euclidean space generalizes this to other problems of interest to [[statistical mechanics]]. Any probability distribution which obeys a condition on correlation functions called [[reflection positivity]] leadleads to a local [[quantum field theory]] after [[Wick rotation]] to [[Minkowski spacetime]]. The operation of [[renormalization]] is a specified set of mappings from the space of probability distributions to itself. A [[quantum field theory]] is called renormalizable if this mapping has a fixed point which gives a quantum field theory.

==See also==