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

 

 

reaction 1+2=3+4

 

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