What Are Feynman Diagrams and How Are They Used in Physics?

[unscientific]

Homework Statement

(a) e- + e+ -> e- + e+
(b) e- + e- -> e- + e-
c) e- + e- -> e- + e- + u+ + u-
d) y -> e+ + e-
e) y + y -> y + y

Homework Equations

The Attempt at a Solution

Part (a)[/B]

Part (b)

Part (c)

Part (d)

Part (e)

Not sure what to do with this, since usually the squiggly lines serve as the 'internal line' or 'virtual particle'.

 

[Orodruin]

None of them are correct. The first one has the wrong direction on the fermion flow of the incoming positron. In the others you either have the wrong process (b) or vertices that do not exist in QED (c) or the process is not happening in the presence of matter as stated (d).

 

[unscientific]

None of them are correct. The first one has the wrong direction on the fermion flow of the incoming positron. In the others you either have the wrong process (b) or vertices that do not exist in QED (c) or the process is not happening in the presence of matter as stated (d).

My notes don't really explain how these diagrams are drawn and my course doesn't delve into too much detail as it is left for grad work.

Why does the positron in the first one have the wrong direction? I thought as an anti-particle it is traveling in the opposite direction?

What are the "rules" that tell us how to draw these diagrams?

 

[Orodruin]

What are the "rules" that tell us how to draw these diagrams?

1. Fermion lines never change direction (caveat: not in the Standard Model anyway)
2. The only allowed vertex is the one you have in (b) and (d). (For all flavours of leptons.)
3. External fermion lines are particles if the arrow points in the "right" direction, i.e., into the diagram if incoming and out of the diagram if it is outgoing. Otherwise it is an anti-particle. (In your (a), the incoming positron points into the diagram, it should be pointing out.)

 

[unscientific]

1. Fermion lines never change direction (caveat: not in the Standard Model anyway)
2. The only allowed vertex is the one you have in (b) and (d). (For all flavours of leptons.)
3. External fermion lines are particles if the arrow points in the "right" direction, i.e., into the diagram if incoming and out of the diagram if it is outgoing. Otherwise it is an anti-particle. (In your (a), the incoming positron points into the diagram, it should be pointing out.)

Thanks a lot for clarifying the rules, that was very helpful. I've updated the diagrams to be:

Part(a)

Part (b)

Part (c)

Part (d)

What do they mean by in the presence of matter?

Part (e)

 

[Orodruin]

(b) now violates rule 1. The fermion line must keep its direction after the vertex.

(c) violates rule 2. You cannot have a vertex with only a fermion line and a photon line attached. Additionally, you have no external muons. You can remedy both of these errors in the same way.

(d) the reaction cannot happen in vacuum because of momentum conservation. In order for momentum conservation to hold, some momentum must be taken from a nearby electromagnetic field due to the presence of background matter.

(a) and (e) are ok.

 

[unscientific]

(b) now violates rule 1. The fermion line must keep its direction after the vertex.

(c) violates rule 2. You cannot have a vertex with only a fermion line and a photon line attached. Additionally, you have no external muons. You can remedy both of these errors in the same way.

(d) the reaction cannot happen in vacuum because of momentum conservation. In order for momentum conservation to hold, some momentum must be taken from a nearby electromagnetic field due to the presence of background matter.

(a) and (e) are ok.

Part (b)

Part (c)

I'm not sure how to do this, but I am guessing:

Part(d)

I'm not sure how to reflect this 'borrowing' of momentum in the diagram. Does it mean creating another virtual particle? So 2 squiggly lines to a vertex then branches out to e- and e+?

 

[Orodruin]

(b) You cannot change it by just changing the arrow. While it did become a valid Feynman diagram, it no longer represents two ingoing electrons. When you changed direction of the line, you traded the electron for a positron.

(c) No. Stop guessing and think about it for some time. There is no vertex with three photons so it violates the rule about the only possible vertex. Make sure to check all rules!

(d) It would be represented by an external photon taken from the external field. This is typically represented by a photon line ending in a point with a cross.

 

[unscientific]

(b) You cannot change it by just changing the arrow. While it did become a valid Feynman diagram, it no longer represents two ingoing electrons. When you changed direction of the line, you traded the electron for a positron.

(c) No. Stop guessing and think about it for some time. There is no vertex with three photons so it violates the rule about the only possible vertex. Make sure to check all rules!

(d) It would be represented by an external photon taken from the external field. This is typically represented by a photon line ending in a point with a cross.

Part (b)

This represents an electron-electron scattering process, not sure what's wrong with this:

Part (c)

Not sure if this is right, but I obeyed the 'one squiggly-two straight lines rule':

Part (d)

 

[Orodruin]

(b) and (c) are correct. Note that there are also more possibilities for (c) that are different from this one. (This also goes for (a).)

On (d) you misunderstood me. You must add an additional external photon. It is in the end of this photon you put a cross, not in a vertex. This represents that the photon is taken from the background.

 

[unscientific]

(b) and (c) are correct. Note that there are also more possibilities for (c) that are different from this one. (This also goes for (a).)

On (d) you misunderstood me. You must add an additional external photon. It is in the end of this photon you put a cross, not in a vertex. This represents that the photon is taken from the background.

So part (d) is:

 

[Orodruin]

No, as I said, the cross is in the free end of the additional photon, not in the vertex. This represents taking it from the external field.

Squiggly external lines represent internal photon propagators or external photons. There is nothing intrinsically linking them to being virtual. Fermions can also be virtual and internal lines.

To be honest, I do not see the point of trying to make students trying to randomly draw Feynman diagrams without telling them at least the very basics of what they represent ...