Wick's theorem

Wick's theorem is a method of reducing high-order derivatives to a combinatorics problem. It is named after Gian-Carlo Wick. It is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. This allows for the use of Green's function methods, and consequently the use of Feynman diagrams in the field under study. A more general idea in probability theory is Isserlis’ theorem.

For two operators ${\displaystyle {\hat {A}}}$ and ${\displaystyle {\hat {B}}}$ we define their contraction to be

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