Not PARTICLES! QUANTA! Is that really all we can accurately state? It's the majority view in physics. Real particles are excitations of fields and virtual particles are fluctuations. The real particles are what we observe in the lab, in scattering processes, while virtual particles are just mathematical trickery to calculate what we observe in relation to the real particles. Now if this were so then also real particles would be math.
What is an excitation? A field is just a mathematical aid which consists of distributions assigned to all points of spacetime, and these distributions have operators as "value". These operators are creation and annihilation operators. These operators create or annihilate one particle states in so-called Fock-space, a direct product of single particle Hilbert spaces. A free particle field is just a particle with a single momentum state or, when localized, a normalized superposition of a spectrum. In a Feynman diagram, there is one line only and begin and end state have the same momentum. The particle is localized if it has a spectrum of momenta. If it has a well defined position though there are infinite associated momenta, due to uncertainty.
There are no such things as pointparticles, no creation and destruction of particles (only couplings), and the virtual particle math scheme is referring to something real. One week ago I actually got suspended for a week on a physics forum because I argued against point particles, the existence preons, the existence of hidden variables, and real existence of virtual particles (which real particles are in fact too, but with related E and p). Low quality contribution. Of course. From the mainstream POV.
So, what is a particle? A particle is a tiny geometrical Planck-sized structure on which charge can safely reside, without leaking out. The extra space dimensions in which it exists are perpendicular to the 3D bulk and this ensures that the Planck length is Lorenz invariant (for which physics still has no answer...). The smallest measurable distance (the Planck length) follows naturally from the particles small extension in space. Within the bounds of the wavefunction (the temporal cross section of a field) the particle just hops around erratically if you propagate it in time. Which is to say it travels on tiny parts of all paths Feynman talks about, coupling to the timeless virtual field to reach others, and being itself a time extended virtual particle with its antiparticle component somewhere in space.