Spin-helicity formalism for gluon-gluon amplitudes

[Silviu]

Hello! In Schwarz's QFT he introduces in chapter 27 the Spin-Helicity formalism as a way of calculating gluon-gluon interactions much easier than going through all the Feynman calculus from the beginning to the end. It seems so amazing, but I am not sure I understand what is the fundamental difference between the 2 approaches that makes one a lot easier than the other. The main difference (on which spin-helicity formalism is actually based) is the fact that momentum is treated like a bi-spinor and not a vector. Why is this approach so much simpler? Can someone give me some intuition to it? Thank you!

 

[LightHero]

The main difference between the two approaches is that, in the spin-helicity formalism, momentum is treated as a bi-spinor instead of a vector. This allows for a much simpler calculation process since the bi-spinor can be used to carry out the calculations more quickly and easily than with a vector. This is because the bi-spinor has two components (the helicity and the spin) which can be used to identify the different parts of the gluon-gluon interaction. This makes it easier to keep track of the different interactions and their respective contributions to the overall result. Additionally, the spin-helicity formalism makes use of the helicity conservation law which states that the sum of the helicities of the two incoming particles must equal the sum of the helicities of the two outgoing particles. This simplifies the calculation process by reducing the number of possible configurations that need to be considered.