Module 2: Relativity and Electrodynamics
Lecture 7: relativistic kinematics
2. Decay of a particle (contd..)
Two-body decay in 4-vector notation
  • Let us now analyze this decay in the language of 4-vectors. There are three 4-momenta:
  • The Lorentz invariants formed out of these 4-vectors are the masses given by
(5)

and the three scalar products and

  • The conservation of 4-momentum,
(6)

gives, when magnitude squared of both sides is taken,

  
(7)

Thus the scalar product can be written in terms of the particle masses. The same is true of the other two scalar products.
  • Thus, given the masses of the three particles, all the physical quantities can be predicted.