Editing Feynman diagram (section)

==== Wick theorem ====
{{Main article|Wick's theorem}}
Because each field mode is an independent Gaussian, the expectation values for the product of many field modes obeys ''Wick's theorem'':

:<math> \left\langle \phi(k_1) \phi(k_2) \cdots \phi(k_n)\right\rangle</math>

is zero unless the field modes coincide in pairs. This means that it is zero for an odd number of {{mvar|φ}}, and for an even number of {{mvar|φ}}, it is equal to a contribution from each pair separately, with a delta function.

:<math>\left\langle \phi(k_1) \cdots \phi(k_{2n})\right\rangle = \sum \prod_{i,j} \frac{\delta\left(k_i - k_j\right) }{k_i^2 } </math>

where the sum is over each partition of the field modes into pairs, and the product is over the pairs. For example,

:<math> \left\langle \phi(k_1) \phi(k_2) \phi(k_3) \phi(k_4) \right\rangle = \frac{\delta(k_1 -k_2)}{k_1^2}\frac{\delta(k_3-k_4)}{k_3^2} + \frac{\delta(k_1-k_3)}{k_3^2}\frac{\delta(k_2-k_4)}{k_2^2} + \frac{\delta(k_1-k_4)}{k_1^2}\frac{\delta(k_2 -k_3)}{k_2^2}</math>

An interpretation of Wick's theorem is that each field insertion can be thought of as a dangling line, and the expectation value is calculated by linking up the lines in pairs, putting a delta function factor that ensures that the momentum of each partner in the pair is equal, and dividing by the propagator.