[Richard777 (OP)]

Two particles interact. Momentum is exchanged during the interaction. The interaction is elastic, each particle recoils at some angle.

Momentum may be represented as a vector. The interaction may be represented as a set of momentum vectors. The vectors are grouped into time phases, an initial phase and a final phase, representing the beginning and end of the interaction.

Each phase has two vectors, one vector for the momentum of each particle. Total momentum is conserved. Vector magnitudes will give the conservation rule. Three rules govern the interaction.

An interaction of special interest is between an electron and a photon as represented by the Compton equation, published in 1923. Energy is transferred from the photon to the electron. The collision is elastic and each particle recoils in a different direction. Vector magnitudes will give the Compton equation.
 
Mass dilation and De Broglie momentum may be included in the Compton equation.

Components of phased momentum may correspond to a Feynman diagram (see attachment).