I'm specifically thinking about quasiphotons as the superposition of photons and other interacting particles when light is traveling through a medium. I've been told there's a fundamental difference between this and composite particles such as protons and neutrons. But what is the difference exactly? They're both the result of other particles/quantum fields interacting and wavefunctions interfering with each other, right?
Im an effort to figure this out, I've been looking up quasiparticles, trying to find an actual formal definition, but I just found a bunch of vague descriptions of emergent phenomena, mostly in classical physics, such as phonons and holes (i.e. electrons and holes in a semiconductor). Those sound only vaguely related to the idea of a quasiphoton as the superposition of other particles (or, technically, the superposition of their wavefunctions) in that they're both emergent phenomena.
So, is there even a formal definition of quasiparticle, at least on the context of QFT and/or particle physics? Or is it just some vague term used to describe anything that's sort of like a particle, but not actually one?
But in that case, what's the formal definition of "particle" in QM, QFT, and/or particle physics? Is it that particles are Fourier transforms of wavefunctions (i.e. wave-packets), while quasiparticles are only superpositions of wavefunctions? That doesn't seem quite right though, because I see no reason a superposition of wavefunctions can't also be the Fourier transform of another wavefunction. If anything, if I understand correctly, in QM the whole point of the FT is to convert between the position and momentum spaces anyway, and I see no reason we couldn't do that with a quasiphoton.
By the way, I've already seen this question: Is differentiating particle and quasiparticle meaningless? but the single answer seems to constantly go back and forth between "yes they're the same" and "no they're actually not", without coming to a definitive answer or making it clear why there isn't one (other than saying they're the same mathematically, but have different physical properties, which makes no sense, as the entire point of the math is to model the physical properties)
I also looked at this one: Is a quasiparticle just an eigenstate of the Hamiltonian? but the single answer uses a lot of notation I'm unfamiliar with so I don't understand most of it (I've mostly self-studied QM on and off for the past few years and I'm only just now finally taking an actual class that will help me understand more of the math, but it's only just started). I'm hoping for a more qualitative/conceptual explanation, but that still makes clear the specific differences.
Alternatively, if that's not reasonably possible, could you stick to math that someone with an engineering degree but who hasn't formally studied a lot of advanced physics would be familiar with? Specifically, I've taken all required undergrad math courses up through diff eq, advanced linear algebra, and statistics, as well as the standard 3 semesters of university physics, as well as electrical engineering courses on electromagnetics and introductory semiconductor physics. What QM I know, aside from the basics covered in physics 3 and the semiconductors course, is primarily from watching lots YouTube videos from reputable physics education channels, which got me familiar with the high-level concepts but left out most of the mathematical details, as well as posting hundreds of questions about QM on Quora over the past 3-4 years, asking specific questions to a friend with a master's degree in physics, and doing about half of Brilliant.org's "Quantum Objects" course.