# 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??

Last edited:
Related Quantum Physics News on Phys.org

"Some questions on the Dyson expansion of the S matrix"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving