How it exists here is in the sense of the qualities it typically possesses–things like form, size, etc., that would account for the behavior associated with it.
I think regarding quarks the question of what it is, or more precisely what are its qualities, cannot be answered through mathematical processes. The only way that I’m aware of at arriving at a reasoned conclusion about what it is when it comes to unobservable physical objects is through abductive reasoning, i.e., following the evidence where it leads.
What exactly do you mean? Wave function, for example, as I understand it is how the mathematical function Ψ describing quantum behavior is labeled in the English language. If that’s what you’re talking about, what I’m referring to is describing how quantum objects exist in the sense of their qualities. As far as I can tell that’s not the same issue as labelling formulas and functions.
Some words that come to mind are wave, particle, point like, spherical or globe like. I believe those are the common descriptions used to refer to subatomic substances. Since we can’t actually observe them, those are the closest approximations we can come up with based on what we know that have at least some explanatory power in regards to the behavior associated with them.
As far as quantum physics is concerned I would agree with you in the sense of the traditional understanding of science. That is why when it comes to describing what it is, when what it is cannot be observed, my view is that it’s more of a metaphysical question. Science focuses on the empirically verifiable. In the traditional sense to scientifically answer the question of what it is requires observation.
That’s why when attempting to answer the question of what it is for something that cannot be observed, it seems to me that the question moves from the realm of physics into the realm of metaphysics where logic and reason come to the fore through abductive reasoning, i.e., following the evidence where it leads.
Just to be clear, I’m assuming with the question above, you’re asking what do abstract mathematical objects that focus on what it does have to do with what it is when determining the qualities of unobservable physical causes, right?