I have seen many papers that discuss the production or decay of mesons
( quark bound states ) to make use of the covariant projection method
where the product υˉu of the quark spinors that are
about to create the mesons is replaced by some dirac operators:
I have seen it in two forms:
1) 1√2⧸ϵ⧸P+M2
and
2) 1√8(M2)3(⧸P2−⧸q−M2)γi(⧸P2+⧸q+M2)
Where
P is the four momentum of the meson, q is the relative momentum
of the quarks and M is the mass of the meson.
Are they different and if yes what different purpose do they serve?\
Moreover I am trying to show the first. To be exact I want to show
(equation (2.1a) here) :
υ(↑)ˉu(↑)=1√2⧸ϵ(↑)⧸P+M2
If I write the spinors as
υ(↑)=(√p⋅σ(01)−√p⋅ˉσ(01)) ,
u†=((10)√p⋅σ,(10)√p⋅ˉσ)
I can't get past the square roots.
Also is it ϵμ(↑)=(0,1,ı,0) ?
Thank you! Any hint would be appreciated.
This post imported from StackExchange Physics at 2015-08-27 17:49 (UTC), posted by SE-user Lefteris