Questions tagged [wick-theorem]

A combinatoric procedure in QFT of reducing arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. A string of such operators is rewritten as the normal-ordered product of the string, plus the normal-ordered product after all single contractions among operator pairs, plus all double contractions, etc., plus all full contractions.

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Why do we have $[\phi_1^+,:\phi_2\phi_3:]=:[\phi_1^+,\phi_2^-]\phi_3:+:\phi_2[\phi_1^+,\phi_3^-]:$?

How $$[\phi_1^+,:\phi_2\phi_3:]=:[\phi_1^+,\phi_2^-]\phi_3:+:\phi_2[\phi_1^+,\phi_3^-]:$$ with $\phi_i=\phi(x_i)$ field operators ($\phi_i^+$ is the annihilation part while $\phi_i^-$ is the creation ...
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Feynman diagrams - swapped only by vertex label

Consider as an example $\phi^3$ theory, which contains at second order both the contractions: $$\newcommand{\mean}[1]{\langle #1 \rangle} \mean{\hat a_q \phi(\color{red}{x})}\mean{T\phi(x)\phi(x)}\...
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Truncation of the product of operators

Given that the operators $A,B $ and $C$ commute with each other, how can we justify the following approximations: $<ABC> ≈ <A><BC> + <AB><C> + <AC><B>$ - 2$&...
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Can I Wick-contract terms with derivatives with terms without derivatives?

Consider for example the QCD three point vertex, can I contract a gluon field with the gluon field with a derivative in the vertex?