Here we are dropping all factors of c. This is based on the freedom to find a set of units where c=1.
The 4-vectors are 4-compoment objects that transform under the Lorentz transformation as a vector.
Boost along the x-directions.
Is an invariant under boosts.
You can define a 4-vector momentum
· is the usual three momentum
· E is the energy
is an invariant.
Let us evaluate this in a general frame
What is this in the rest frame of the particle?
and we identify the energy for a particle at rest as the mass energy
Energy and momentum conservation
Suppose a particle decays into n particles
Suppose you identify the three particle in the final state so that you know their rest masses.
For two particles