Keywords: covariance, energy–momentum 4–vector, relativistic frame invariants, relativistic systems, particles, particle physics, inelastic collisions, elastic collisions, theorem of conservation of momentum, theorem of conservation of total energy, nuclear accelerators
Covariant treatment of collisions in particle physics
The use of relativistic frame invariants is very well established, especially when it comes to the energy–momentum. In the current paper we show how the conservation of the energy and momentum applies to collisions of particles moving at relativistic speeds, like the ones encountered in nuclear accelerators. We derive the equations for two main types of collisions: elastic and inelastic. The starting point in both cases is the well known theorems of conservation of total energy and conservation of momentum for isolated systems. The covariance, once proven, becomes a very useful tool due to the fact that researchers can use any inertial frame in solving the particle collision problems, thus greatly simplifying the solutions.