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

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Discussion Overview

The discussion revolves around the conventions for representing anti-fermions in Feynman diagrams, particularly focusing on the direction of arrows used to indicate these particles. Participants explore whether these conventions are dictated by fundamental physics principles or if they are merely stylistic choices. The context includes teaching practices in quantum mechanics and the implications for student assessments.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant recalls that anti-fermions are typically drawn with arrows pointing in the opposite direction to fermions, citing this as a basic rule for Feynman diagrams.
  • Another participant emphasizes that the direction of arrows is significant, as it relates to the Dirac spinors used in calculations.
  • A question is posed about academic standards, specifically whether a student would lose credit for incorrectly drawing anti-particles with arrows pointing forwards.
  • A participant shares their experience of losing points for such an error in a quantum mechanics course.
  • It is noted that the key rule is consistency in the direction of arrows along fermion lines, allowing for flexibility in interpreting time direction and particle types.
  • One participant suggests that in the context of beta minus decay, the anti-neutrino and electron lines can be viewed as forming a continuous path through the interaction vertex.
  • Another contribution states that the direction of arrows is a convention for drawing Feynman diagrams and that amplitudes are calculated based on these arrows, with the Stuckelberg-Feynman interpretation allowing for incoming representations of anti-fermions.

Areas of Agreement / Disagreement

Participants express differing views on whether the direction of arrows for anti-fermions is a matter of convention or if it has a deeper physical significance. There is no consensus on a definitive answer to the question posed regarding the necessity of following these conventions.

Contextual Notes

Some participants highlight that the discussion involves assumptions about the interpretation of Feynman diagrams and the implications for teaching and assessment in quantum mechanics. The conversation reflects a lack of clarity on whether the conventions are universally accepted or subject to personal interpretation.

MalachiK
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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?
 
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It's not a decoration; it has meaning - the arrows tell you what Dirac spinors to use: u, vbar, ubar or v.
 
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?
 
When I was taking QM, I did just that, and the professor took off points.
 
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.
 
Bill_K said:
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?
 
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.
 

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