I am very confused by the statement made in Haag's, Local Quantum Physics: Fields, Particles, Algebras (page 46):
... the idea that to each particle there is a corresponding field and to each field a corresponding particle has also been misleading and served to veil essential aspects. The rôle of fields is to implement the principle of locality. The number and the nature of different basic fields needed in the theory is related to the charge structure, not the empirical spectrum of particles. In the presently favoured gauge theories the basic fields are the carriers of charges called colour and flavour but are not directly associated to observed particles like protons.
However, in my understanding of the SM, to each field (or linear combination of) we do assign a particle, even if we do not directly observe it. So, even though I agree that there is no field in the SM which corresponds to the proton, there is a field corresponding to the quarks, which we do not observe on their own. In fact, it seems to me that we define the notion of fundamental particle by the fact that there is a field associated to it.
Another aspect of this discussion may be that, once we have the full SM, the relationship between fields and the symmetry groups is what defines the particle. Quarks are described by the multiplet of fields that transform non-trivially into each other under the $SU(3)$ gauge symmetry.
Can somebody help me understand more clearly what Haag is referring to in this quote from his book? Thank you very much.