I think you are distracted by dubious interpretational remarks that particles are probability waves or that they are excitations of the field. I would advise to ignore such remarks, and focus on mathematical structure. Particles are what they are, physical somethings. Since such somethings are physical, they are distinct from the mathematics which we use in physics. Mathematics (at least in its pure form) is a product of the human mind and quite distinct from physical reality.
In quantum mechanics we do not actually describe particles. We describe the probabilities for measurement results. This is done using states in Hilbert space. The wave function is simply the components of the state in a particular basis (the basis of position states). Since the state is essentially a description of probability, it changes when information changes, for example when a measurement is performed. Collapse is just a change of information resulting from measurement. 795
To describe states of many particles we construct Fock space from the Hilbert space of states of a single particle.
Quantum fields are operators defined (albeit not rigorously in usual treatments) on Fock space, and describe the creation and annihilation of particles in interaction. In qft we are usually most concerned with describing the effects of interaction, but to bring it back to experiment, we still have to form S-matrix elements and calculate cross-sections using initial and final states. These are still states in Hilbert space, and collapse still takes place for the states when a measurement is performed.
There are important generalisations, however. For example, in elementary treatments of quantum mechanics, one may take the <PERSON> projection postulate as axiomatic for the treatment of observable quantities, meaning that collapse always takes place in measurement. This is not generally true in quantum field theory. For example we cannot actually measure the position of a photon, but only the position at which the annihilation of a photon took place. Consequently, the projection postulate does not apply. Also we can regard the expectation of the photon field as the classical electromagnetic $A$ field. The $A$ field is strictly not observable, but the derivatives, the $E$ and $B$ fields are generally considered as observable quantities. There is no collapse when we observation is of the expectation of an observable, as distinct from elementary qm in which observable quantities are treated as eigenstates of observable operators.
For this reason the <PERSON>–von Neumann axioms (as given in Wikipedia) make no mention of eigenstates and eigenvalues (implicit in collapse) but only use expectations of observables, from which it is possible to show that eigenstates and eigenvalues are a special case.
I have given a rigorous treatment in A Construction of Full QED Using Finite Dimensional Hilbert Space, and a fuller account in my books (see profile). 800