Here we are dropping all factors of c. This is based on the freedom to find a set of units where c=1.

_{}

- Combine position and time into a 4-vector.
- Define covariant and contravariant vectors for inner product
- Define the metric

_{}

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

_{}

_{}is_{}three vector dot product.

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

_{}