My understanding so far:
A wave is a vector field defined on the space-time. i.e. mathematically wave is just a mapping which for every point in the space-time maps it to a vector.
A world-line is function which maps an event (or a particle) on the space-time. In case the event (or the particle) "exists" only for an instant then the world-line will just be a point in the space-time diagram.
A few questions now (basically I want to check if I understand the concepts correct as I self-study these topics):
Q1 - Are the above definitions correct (and generic enough)?
Q2 - Based on above then (and if they are correct) there is nothing like a world-line of a wave. I'm getting quite confused here (maybe I'm unable to visualize) but it appears to me that only "particles" can have world-lines defined