Exploring Peskin & Schroeder's QFT Propositions on p. 166

[gremezd]

It would be nice if someone commented a couple of propositions by Peskin and Schroeder in their QFT book in p.166.

There they say that when the helicity is conserved in the high energy Compton scattering, one unit of spin angular momentum is converted to one unit of orbital angular momentum. From the picture in p.166 it is quite obvious that after the collision one unit of spin angular momentum is lost. However, how do we physically interpret the emergence of orbital angular momentum? Do particles begin to orbit?

In the same page it is argued that the final state is a p-wave and that it is somehow related to the conservation of angular momentum. What do they mean by that? And what is a p-wave in this context?

 

[lightarrow]

It would be nice if someone commented a couple of propositions by Peskin and Schroeder in their QFT book in p.166.

There they say that when the helicity is conserved in the high energy Compton scattering, one unit of spin angular momentum is converted to one unit of orbital angular momentum. From the picture in p.166 it is quite obvious that after the collision one unit of spin angular momentum is lost. However, how do we physically interpret the emergence of orbital angular momentum? Do particles begin to orbit?

In the same page it is argued that the final state is a p-wave and that it is somehow related to the conservation of angular momentum. What do they mean by that? And what is a p-wave in this context?

p-wave = polarized wave; in this case I assume it's circular polirized.

 

[Entropia]

I can provide some insight and clarification on the propositions mentioned in Peskin and Schroeder's QFT book on p. 166.

Firstly, the conservation of helicity in high energy Compton scattering refers to the conservation of the projection of the particle's spin along its direction of motion. In this process, there is a transfer of energy and momentum between a high-energy photon and a particle, such as an electron. The conservation of helicity means that the total spin projection before and after the collision remains the same.

The statement about the conversion of one unit of spin angular momentum to one unit of orbital angular momentum is referring to the fact that in high energy Compton scattering, the final state particles can have orbital angular momentum in addition to their spin. This is because the particles are in motion and can have a non-zero angular momentum due to their motion around the center of mass of the system. This is a consequence of the conservation of total angular momentum in the system.

In terms of physical interpretation, the emergence of orbital angular momentum does not necessarily mean that the particles begin to orbit. It simply means that the particles have additional angular momentum due to their motion in the system. This can be visualized as a spinning top, where the top's spin is its intrinsic angular momentum and the motion around its axis of rotation is the orbital angular momentum.

The statement about the final state being a p-wave is related to the angular momentum of the system. In quantum mechanics, particles can have different wave functions, which can be described by different quantum numbers. The p-wave refers to the wave function of the particles having a non-zero orbital angular momentum, specifically, a value of 1. This is related to the conservation of angular momentum, as mentioned earlier.

In summary, the propositions mentioned on p. 166 in Peskin and Schroeder's QFT book describe the conservation of angular momentum and the emergence of orbital angular momentum in high energy Compton scattering. These concepts are key in understanding the behavior of particles at high energies, and they have been extensively studied and confirmed through experiments.