Is the Feynman diagram in The Big Bang Theory episode correct?

[Basip]

Dear community!

I watched The Big Bang Theory and watched this episode. If you click on it you would get to a homepage - if you scroll down you would get to a section called Episode Questions -> Physics Bowl. According to the newspapers The Big Bang Theory have an employee who is scientist (Chemist or Physicist). He check all the formulas in the show.

But I think the Feynman diagram is correct, but the corresponding equation is wrong. And the result is wrong too. Would you say I am right with it?

But how would the correct formula be? And how would the answer be? I am just really curious!

Kind regards!

Here the formula from the show:

$$\left ( 2 \pi \right )^4 \int \left [ \bar{v}^{(s_2)} \left ( p _3 \right ) \left (i \sqrt{4 \pi \alpha}\gamma^\mu \right ) v^{(s_1)} \left ( p _1 \right ) \right ] \frac{i g_{\mu\nu}}{q^2} \left [ \bar{v}^{(s_4)} \left ( p _4 \right ) \left ( i \sqrt{4 \pi \alpha}\gamma^\mu \right ) v^{(s_2)} \left ( p _2 \right ) \right ] \times \delta ^{(4)} \left (p _1 - p _3 - q \right ) \delta ^{(4)} \left ( p _2 + q - p _4 \right ) d^4 q$$

PS! If you need the formula and the Feynmandiagram in a better quality, you can find it here in LaTeX.

 

[jedishrfu]

The Numb3rs show was like this. A prof would write stuff on the board so Charlie would look smart. The math didn't always fit well with the show as it was added in after the story was developed.

 

[BvU]

Dear Basip,
I didn't watch the show. Did follow your instructions and found your answers right underneath (towards the end of Physics Bowl). See Peskin and Schroeder page 131.