Dirac Spinors Suck: QFT Calculations with Weyl Spinors

In summary, the conversation discusses the challenges of using Dirac Spinors in QFT and the benefits of using Weyl Spinors. The reference to a paper that explains how to do calculations with Weyl spinors is also mentioned. The conversation also expresses appreciation for the paper and discusses the potential impact it could have had if it was available earlier.
  • #1
BenTheMan
478
0
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
 
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  • #2
Thanx for the reference :-)
 
  • #3
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.
 
  • #4
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...
 

1. What are Dirac spinors and how are they used in QFT calculations?

Dirac spinors are mathematical objects used in quantum field theory (QFT) to describe the quantum states of spin-1/2 particles, such as electrons. They are solutions to the Dirac equation, which is a relativistic wave equation that describes the behavior of particles with spin. In QFT calculations, Dirac spinors are used to represent the quantum states of fermionic particles and to calculate their interactions with other particles.

2. How do Dirac spinors differ from Weyl spinors?

Dirac spinors and Weyl spinors are two different types of spinors that describe different types of particles in QFT. Dirac spinors describe fermions, which have half-integer spin, while Weyl spinors describe massless particles, such as photons, that have integer spin. Mathematically, Dirac spinors have four components, while Weyl spinors have only two components.

3. Why are Weyl spinors sometimes preferred over Dirac spinors in QFT calculations?

Weyl spinors are sometimes preferred over Dirac spinors in QFT calculations because they simplify the calculations by reducing the number of components needed to describe a particle state. This is especially useful when working with massless particles, such as in the study of high-energy physics or cosmology.

4. What are some challenges in using Dirac spinors in QFT calculations?

One challenge in using Dirac spinors in QFT calculations is that they can be mathematically complex and require advanced mathematical techniques to manipulate and solve equations. Additionally, in some cases, the use of Dirac spinors can lead to divergent results, which require special techniques, such as renormalization, to be accounted for in the calculations.

5. How are Dirac spinors related to the Dirac equation and the standard model of particle physics?

The Dirac spinors used in QFT calculations are related to the Dirac equation, which is a fundamental equation in quantum mechanics that describes the behavior of spin-1/2 particles. The Dirac equation is also a key component of the standard model of particle physics, which is a theoretical framework that describes the fundamental particles and their interactions. In the standard model, the Dirac spinors represent the quantum states of fermionic particles, such as quarks and leptons.

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