We draw the positron as if it's traveling backward in time. Why? The momentum of the positron is drawn opposite to the time-direction of the diagram. I don't see this having any effect on the calculation. We still arrive at the result $k=p_1+p_2$, and not $k=p_1-p_2$ like the diagram would indicate. So, if anything, the diagram is misleading? $p_1$ and $p_2$ are the momenta of the incoming electron and positron, $k$ is the momentum of the virtual photon.
$\begingroup$
$\endgroup$
5
-
1$\begingroup$ Who are we? Which page? $\endgroup$– Qmechanic ♦Commented Jul 7, 2022 at 8:06
-
$\begingroup$ @Qmechanic Diagram of type 1 Bhabha process. The incoming positron is drawn to have a momentum opposite to the time direction $\endgroup$– Ryder RudeCommented Jul 7, 2022 at 8:10
-
$\begingroup$ Perhaps related; see also. $\endgroup$– rob ♦Commented Jul 7, 2022 at 9:42
-
$\begingroup$ @rob Can we say that the arrows in the Feynman diagrams have no effect on the calculation? They're just there to indicate that electron and positron are similar beasts? Also, if a positron backwards arrow is labelled by a three momentum $\vec{p}$, then I should not conclude that its actual three momentum is $-\vec{p}$, right? $\endgroup$– Ryder RudeCommented Jul 7, 2022 at 9:47
-
1$\begingroup$ Both correct. The arrows make it easier to conserve lepton number at each vertex. $\endgroup$– rob ♦Commented Jul 7, 2022 at 9:52
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
The arrow direction in a Feynman diagram does not correspond to the time direction. There are conventions in which times flows from left to right, i.e. the time on the left is always earlier than the time on the right, although these are not the most common ones. Regardless of the convention, the arrow direction is just used to distinguish different kind of particles, for examples electrons from positrons or electrons from holes.
The momentum of the particle is also usually independent from the arrow direction, although also this may depend on the convention used. For example in non relativistic many body perturbation theory, the momentum usually refers to the one of the state on the band structure. Then the electron has the same momentum, while the hole has opposite momentum compared to the one written in the diagram.
On the time direction. Real particles never travel backward in time. For virtual particles instead this can happen. For example you can have an initial particles which goes from say $t_0$ to $t_1<t_0$, then interacting with a photon for example, and propagate from $t_1$ to $t_2>t_0$. Indeed $t_1$ would be an integrated variable, and all the possible values of $t_1$ need to be considered. In the convention where time flows from left to right, and for the case $t_2<t_1$, there would be a line from center to the left, and a second line going back from the left to the right. In both lines the direction of the arrow would just depend on the particle kind, and not on the time flow.
However, also in case of virtual particles, one should be careful when saying that something goes back in time. It is a fashinating concept, but also one which generates a lot of confusion.
