# Some questions on the Dyson expansion of the S matrix

#### robousy

I have some questions regarding:

$$S = \sum_{n=0}^\infty\ S^n = \sum_{n=0}^\infty \frac{i^n}{n!} \idotsint \ {d^4x_1}\ {d^4x_2} \dots \ d^4x_n \ T (H_I(x_1) \ H_I(x_2) \dots \ H_I(x_n) )$$

1) What is n? How do you pick n given some interaction? ( I think it might be the order in perturbation theory...)

Now, consider the QED interaction:

$$H_I(x)=-eN({\overline{\psi}(x) \def\lts#1{\kern+0.1em /\kern-0.65em #1} \lts{A}(x) \psi(x) )$$

Now

2)I know I have to go to n=2 here and use Wicks theorem here and do some contractions...but I don't really understand what to contract or how to do it.

3) Is Wicks theorem used because its the only way we know how to work out Time ordered Normal products?

4) Is everything considered a field, ie are $$\psi , \overline{\psi} \: and \: \Its{A}$$ all considered fields.

5) Can I express contractions in Latex? If so how please??

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