This is the table of elementary particles in the standard model of particle physics:
The model is called standard because it describes the grand majority of existing data and has been predictive of new phenomena, as the discovery of the Higgs boson.
The standard model lagrangian develops a field theory of interactions for these particles, the measurable quantities defining integrals represented by Feynman diagrams.
For each particle in the table a field over all (x,y,z,t) is postulated on which creation and annihilation operators define the particles, so there exists in all of space a photon field , an electron field,... and thus a Higgs field.
If an extension of the standard model in the future has more elementary particles, including more Higgs ones, these also will be defined over all space on which the corresponding creation and annihilation operators will operate.