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I am having trouble understanding the Antisymmetrization rule given in Griffith's book for the calculation of amplitude which states that "include a minus sign between diagrams that differ only in the exchange of two incoming (or outgoing) electrons (or positrons) or of an incoming electron with outgoing positron (or vice versa).

Now in electron-positron scattering, it is said that exchange incoming positron with outgoing electron to go from fig 7.5 to fig 7.4 enter image description here

Now if I replace p1 with p3 in fig 7.4 (i.e. an incoming electron with outgoing electron) then also I have a valid different graph and it should follow the antisymmetrization rule, then why this possibility is not taken into account?

Also in compton scattering fig 7.6 I can replace p1 with p4 to get a different diagram.enter image description here

Please tell me where I am wrong in my concept and how to know that, how many different diagrams for the same process (lowest order) will be there which follow antisymmetrization rule for the calculation of amplitude.

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  • $\begingroup$ Note that eectrons and positrons are not identical particles. $\endgroup$ – my2cts Jun 10 at 11:16
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To avoid double counting, it might help to describe the convention Griffiths is using. He's drawing the external $p_1,p_2, p_3, p_4$ lines in fixed positions on the page and then connecting them to a pair of interaction vertices in all possible ways. After the attempt to "cancel" the diagram in Figure 7.4 as you suggest, you will have $p_3$ at the bottom left and $p_1$ at the bottom right instead. This isn't a different diagram but the same one in a different convention.

Let's look at Figure 7.5 now. This has a relative minus sign compared to 7.4 because now $p_2$ (incoming positron) has been switched with $p_3$ (outgoing electron). Why do I say they've been switched? After all, $p_2$ is still top left and $p_3$ is still bottom right as per the convention. Well they've been switched in the sense that $p_2$ is now what shares an interaction vertex with $p_1$ instead of $p_3$.

In general, these conventions are designed to minimize the number of diagrams you have to draw. So it is worth getting used to them even if you have a different intuition for what is "distinct". In particular, one thing you will always see for 2-2 scattering of neutral particles is three diagrams at tree level referred to as the $s$, $t$ and $u$ channels. Once you make some of the particles charged, you will end up with a subset of these channels.

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