momentum: From my limited knowledge of physics, I understand this is as a physical representation of a physical object. But, we aren't that far yet (i.e., causally we are before 'laws' and before 'physical stuff'). What does momentum mean in pure mathematical terms in regards to waves?

Note: I might be grossly misunderstood here. What I mean is that momentum is used as a physical representation of a particular state of a physical object (e.g., a particle).