State how the 4 -momentum of a particle is related to its energy and 3momentum. How is related to the particle mass? For two particles with 4 -momenta and find a Lorentz-invariant expression that gives the total energy in their centre of mass frame.
A photon strikes an electron at rest. What is the minimum energy it must have in order for it to create an electron and positron, of the same mass as the electron, in addition to the original electron? Express the result in units of .
[It may be helpful to consider the minimum necessary energy in the centre of mass frame.]