Wick's theorem allows one to write(adsbygoogle = window.adsbygoogle || []).push({}); a free theory time-ordered ##n##-point correlation functionasa product of free theory time-ordered ##2##-point correlation function.

The procedure involves the pairwise Wick contraction of fields such that external fields are not paired up each other.

Consider the following time-ordered correlation function:

$$\langle 0 | T \{ \phi(x_{1}) \phi(x_{2}) \phi(x) \phi(x) \phi(x) \phi(y) \phi(y) \phi(y) \} | 0 \rangle.$$

This time-ordered ##8##-point correlation function can be Wick contracted in multiple ways.

1. One possible Wick contraction pairs ##\phi(x_{1})## with one ##\phi(x)## and pairs ##\phi(x_{2})## with another ##\phi(x)##.

2. Another possible Wick contraction pairs ##\phi(x_{1})## with one ##\phi(x)## and pairs ##\phi(x_{2})## with one ##\phi(y)##.

3. A third possible Wick contraction pairs ##\phi(x_{1})## with one ##\phi(y)## and pairs ##\phi(x_{2})## with another ##\phi(y)##. However, this appears to be redundant as it is already covered in the first choice of Wick contractions. Am I wrong?

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# A Free theory time-ordered correlation function with two internal fields

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