Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one.
On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of a "harmonic paradigm". He uses this term to describe physical theories which are based on studying the excitations of a field, like QFT and String theory do. He is surprised by the fact that even after 75 years we still rely on basic notions of oscillations and wave packets for our physical theories and have not yet found an alternative formulation.
My questions are:
What makes this "harmonic paradigm" so useful?
What, if any, alternative formulations have been proposed?