There can be three ways, two particles colliding and interacting as waves, temporarily superimpose and cancel part of their wave components and collapse,
The oscillatory components of the waves in the same direction and opposing phase, or in opposing directions but in phase, will cancel when superimposed and so temporarily collapse the resultant wave. This is type 1.
In type 2 collision, the velocity component along a time dimension of the wave cancels. Assuming that it is possible to cancel the velocity component of the wave along a time dimension. Although the time dimensions are not accessible to us as the three space dimensions, it is still be possible to orientate the wave component triplets, which forms a orthogonal corner, such that the time dimensions of the colliding waves at light speed, are in opposing directions.
In type 3 collision, both oscillatory component and the velocity component of the wave cancel.
Collapsing the wave temporarily allows the components of the wave to be reshuffled and so create a new type of particle after the collision.
Creation, but first destruction, temporarily...