I Off-shell on-shell

1. Dec 14, 2016

Lapidus

Here they say that if you add two momentum vectors of two on-shell particles, you get an off-shell particle.

Two questions:

1. Since on-shell solutions are solutions to the free equation of motion, should no adding two solutions also give a solution?

2. Why should adding two on-shell particles represent an interaction?

thank you

2. Dec 14, 2016

Staff: Mentor

Not necessarily (you can produce a heavier particle if the energy matches), but this is a typical result.
The opposite direction: If they interact to form a new particle, then you have to add the momenta. There are other interactions where the sum of momenta is irrelevant.