The Wick Theorem provides a systematic method for decomposing time-ordered products of free field operators in Quantum Field Theory into sums of normally ordered terms and contractions. A contraction is formally defined as the difference between a time-ordered product and its corresponding normal-ordered form, resulting in a scalar c-number rather than an operator that satisfies causal commutation relations like $[\phi^+(x), \phi^-(y)]$. This theorem establishes that vacuum expectation values of odd numbers of field operators vanish while even numbers decompose into sums over all possible full contractions, serving as the foundational algebraic rule for calculating perturbative scattering amplitudes via Feynman diagrams.
The Wick Theorem provides a systematic method for decomposing time-ordered products of free field operators in Quantum Field Theory into sums of normally ordered terms and contractions. A contraction…