Required math: calculus
Required physics: special relativity
Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – Chapter 3; Problem 3.3.
As a simple example of the calculation of four-momentum, suppose we have a neutral pion moving at a speed at an angle of in the first quadrant. The rest mass of a is MeV.
The four-momentum is defined as
The angle is chosen because and , so