Inside the World's Largest Science Experiment

Just like you, I didn't take lectures on QFT, I was specializing on solid-state physics in the direction of computer science and then ended in the IT business anyway. But since Hamburg has DESY particle physics was of interest, too.
Yes, it's nice how the wave/particle dualism translates mathematically. You get a glimpse of why a particle can be interpreted as a point in spacetime and as field or wave stretching into infinity when you learn about the Dirac delta function and the Fourier transform. It's a lot of steps into further details to get to field excitations representing particles.