Why Do GUT Theories Only Use Left Spinors?

[Magister]

Why in every single text about GUT theories only the left spinors are used? Why use the conjugate of the spinor instead of the spinor itself? Is it just a another historic definition?

Thanks

 

[Barmecides]

Why in every single text about GUT theories only the left spinors are used? Why use the conjugate of the spinor instead of the spinor itself? Is it just a another historic definition?

I do not know much about GUT theories, but it might be related to the fact we often have majorana particles and it is easier the formulate the them with left spinor, anti-particles and conjugate than with left and right spinors ?

In any case, if you learn about the answer, I am interested about it.

 

[blechman]

Barmecides has it more or less right. The standard model is a Chiral theory (left and right handed fields are treated separately) so it makes sense to write things down in terms of Weyl spinors (2-component). Whether we write them as (1/2,0) fields ("left-handed") or (0,1/2) fields ("right-handed") is a matter of convention, and the convention is to use left-handed fields. There's nothing really special about this, but if you feel like using right-handed spinors, you'll have to do a whole lot of hermitian-conjugating in order to match results with other papers!

Remember: left-handed spinors describe right-handed fields just fine (you just have to use the antiparticle). There's nothing wrong with this. And when all fields are left-handed (or right handed, but as long as it's just ONE of them) - then it's very easy to keep track of what Lorentz-invariant combinations you can write down. Otherwise, you're likely to make a mistake. TRUST ME: I speak with the voice of experience!

 

[Magister]

Ok. That was what I thought. I was just wondering if there was another reason for that.

Thanks a lot for your replies