What is the correct convention for anti-fermions in Feynman diagrams?

[MalachiK]

Hi Guys.

I'm hoping that you might be able to help me out with a question I have about anti-particles in Feynman diagrams. I'm drawing these again for the first time in over a decade because I'm teaching an elementary physics course that requires the students to draw diagrams for a few simple processes. The last time I drew these was when I was an undergraduate and so I don't really have any of the deep background knowledge to convince myself of the right answer.

When I was at university I drew anti-fermions with arrows pointing in the opposite directions to the fermions. I have always assumed that this was one of the basic rules for constructing Feynman diagrams. I've checked this forum and there are plenty of posts ( like this one https://www.physicsforums.com/showthread.php?t=453948) that agree with this backwards anti-fermion construction. Likewise, the hyperphysics website, examples from the CERN education pages etc. all follow the same example. However, the folks that set the exam that my students have to sit have different ideas. All of the questions in their exam require both http://store.aqa.org.uk/qual/gce/pdf/AQA-2450-W-TRB-OGPP.PDF (page 12). The only mention I can find of this discrepancy in the exam information says simply 'some particle physicists write reverse the arrows for anti-particles." This seems quite unsatisfactory - as if the rules for constructing these things are a matter of personal taste - and in any event having them all in the same direction all of the time seems to make the whole exercise of drawing the arrows a bit pointless

So my question is this... Are the directions of the fermion arrows required by underlying phyiscs (CPT symmetry? charge conservation?) to point in specific directions or is this just a convention that we are free to ignore at will?

 

[Vanadium 50]

It's not a decoration; it has meaning - the arrows tell you what Dirac spinors to use: u, vbar, ubar or v.

 

[MalachiK]

Right. So from the point of view of academic standards - if you were teaching a QM course and a student drew anti-particles with arrows in the forwards direction you would withhold credit for that part of the answer?

 

[Vanadium 50]

When I was taking QM, I did just that, and the professor took off points.

 

[Bill_K]

When I was at university I drew anti-fermions with arrows pointing in the opposite directions to the fermions. I have always assumed that this was one of the basic rules for constructing Feynman diagrams.

The basic rule is that all of the arrows on each fermion line must be consistent, i.e. form a continuous path. The nice thing about Feynman diagrams is that you don't have to worry about which direction is forward in time, or which lines represent anti-fermions.

 

[MalachiK]

The basic rule is that all of the arrows on each fermion line must be consistent, i.e. form a continuous path. The nice thing about Feynman diagrams is that you don't have to worry about which direction is forward in time, or which lines represent anti-fermions.

So, am I correct in thinking that in the diagram for beta minus decay the anti-neutrino and the electron lines are considered as forming a continuous path through the vertex with the W-? I'm guessing that it's in some way valid to think of the anti-neutrino entering the diagram, interacting with the W- and then leaving as an electron. Is this what you're getting at?

 

[andrien]

it is just about a convention for drawing feynman diagram and the way amplitudes are written from it.The amplitude is written according to following arrows,for an antifermion since the direction is reversed as compared to fermion,but it still represents an incoming one because of the usual Stuckelberg-Feynman interpretation.