Dirac Spinors Suck: QFT Calculations with Weyl Spinors

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SUMMARY

The discussion emphasizes the challenges faced by Quantum Field Theory (QFT) students when working with Dirac spinors, which can hinder progress for at least a month. It highlights that while Weyl spinors are more sensible for writing the Standard Model, Dirac spinors are often necessary for calculations, especially in vectorlike theories such as Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED). A key reference is provided: the paper available at arxiv.org/abs/0812.1594, which offers insights into using Weyl spinors for calculations. The discussion concludes that familiarity with both spinor types is beneficial for researchers in the field.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT)
  • Familiarity with Dirac spinors and Weyl spinors
  • Knowledge of vectorlike and chiral theories in particle physics
  • Basic concepts of Majorana Neutrinos
NEXT STEPS
  • Read the paper "Weyl Spinors in Quantum Field Theory" available at arxiv.org/abs/0812.1594
  • Explore the differences between vectorlike and chiral theories in particle physics
  • Study the implications of using Dirac spinors in QCD and QED calculations
  • Investigate the role of Majorana Neutrinos in chiral theories
USEFUL FOR

Physicists, graduate students in Quantum Field Theory, and researchers focusing on particle physics who are looking to enhance their understanding of spinor calculations and their applications in various theories.

BenTheMan
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I think that anyone who has done a course in QFT has had their progress hampered by AT LEAST a month by Dirac Spinors. Why is it that the only sensible way to write the Standard Model down is to use Weyl Spinors, but the only sensible way to do calculations is to use Dirac spinors and projection operators?

Jesus, you'd think someone would come up with a way to do calculations with Weyl spinors...

Oh wait! Eureka! Someone has written this all down!

http://arxiv.org/abs/0812.1594
 
Physics news on Phys.org
Thanx for the reference :-)
 
Now, now. While I am certainly a Weyl-spinor fan myself, there are some benefits to knowing both procedures.

Let me say that if you are working with a VECTORLIKE theory of fermions (QCD, QED,...) then you are MUCH better off working with Dirac spinors, they save you a great deal of time and trouble. Those of us (myself included) who work with CHIRAL theories of fermions (EW,BSM,...) would often find Weyl spinors much more convenient.

BTW: EXCELLENT reference, that paper! I know it's been in the works for several years now, I was very happy to see it finally published.
 
Thanks Ben for alerting us to this paper!

I wish that it was around when I started grad school... would probably cleared up a lot of the issues I had with Majorana Neutrinos...
 

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