Editing Normal order (section)

===Wick's theorem===
{{Main|Wick's theorem}}

'''Wick's theorem''' states the relationship between the time ordered product of <math>n</math> fields and a sum of 
normal ordered products. This may be expressed for <math>n</math> even as

:<math>\begin{align}
T\left[\phi(x_1)\cdots \phi(x_n)\right]=&:\phi(x_1)\cdots \phi(x_n):
+\sum_\textrm{perm}\langle 0 |T\left[\phi(x_1)\phi(x_2)\right]|0\rangle :\phi(x_3)\cdots \phi(x_n):\\
&+\sum_\textrm{perm}\langle 0 |T\left[\phi(x_1)\phi(x_2)\right]|0\rangle \langle 0 |T\left[\phi(x_3)\phi(x_4)\right]|0\rangle:\phi(x_5)\cdots \phi(x_n):\\ 
\vdots \\
&+\sum_\textrm{perm}\langle 0 |T\left[\phi(x_1)\phi(x_2)\right]|0\rangle\cdots \langle 0 |T\left[\phi(x_{n-1})\phi(x_n)\right]|0\rangle
\end{align}</math>

where the summation is over all the distinct ways in which one may pair up fields. The result for <math>n</math> odd looks the same
except for the last line which reads

:<math>
\sum_\text{perm}\langle 0 |T\left[\phi(x_1)\phi(x_2)\right]|0\rangle\cdots\langle 0 | T\left[\phi(x_{n-2})\phi(x_{n-1})\right]|0\rangle\phi(x_n).
</math>

This theorem provides a simple method for computing vacuum expectation values of time ordered products of operators and was the motivation behind the introduction of normal ordering.