The conservation of four-momentum in scattering processes is a fundamental theorem within quantum field theory and high-energy particle physics stating that the sum of incoming four-vectors equals the sum of outgoing four-vectors at interaction vertices. This principle relies on Minkowski spacetime geometry, where energy and momentum are unified into a single contravariant vector $P^\mu = (E/c, \vec{p})$ satisfying the invariant mass shell condition $P^2 = m^2$. As a strict kinematic constraint derived from translational invariance via Noether's theorem, it defines the allowable phase space configurations for any relativistic scattering event.
Prerequisite chain context: requires Minkowski Space in Special Relativity.