Wick's theorem is a fundamental result in quantum field theory and many-body physics that provides a systematic way to evaluate time-ordered products of creation and annihilation operators. It essentially allows one to express time-ordered products of operator products in terms of normal-ordered products and their vacuum expectation values.
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Wick theorem expresses a time-ordered product of free fields as its normal-ordered product plus the sum over every possible contraction. It turns the Dyson series into Feynman diagrams.