These fields are initially massless. That is to say, the excitation quanta do not have any intrinsic rest mass; to the extent that they carry mass-energy, it is entirely due to their kinetic energy.
Moreover, these fields share a common property: Their lowest energy state is when the excitations are absent. No particles. Now there is another field added to this mix: The Higgs field. It has a unique property: it is not in its lowest energy state when there are no excitation quanta. The absence of any Higgs excitation quanta, aka. Higgs particles, represents a “false” vacuum: a vacuum that is actually a higher energy state than the state in which some Higgs particles are present. So this vacuum is unstable and quickly decays, by creating Higgs excitation quanta, into a new, “true” vacuum that is really the lowest energy state.
Now comes the trick: we take this new, stable vacuum and redefine everything with respect to it. That is, we redefine the electromagnetic field, the W and Z boson fields, the quark fields, the neutrino fields such that this new, stable vacuum is treated as the, well, vacuum. And we find that we now have new terms in the equations: with respect to this new vacuum, all these fields (with the exception of photons and the gluons of the strong interaction) now behave as though they did have mass! And that, then, is our effective particle content in the universe that we observe: Massive electrons, massive quarks, massive W and Z bosons.
That said, I should hasten to add another important point. When you grab an everyday object and weigh it… approx. 99% of its mass is not due to the Higgs mechanism. Only 1% is due to the quark and electron masses obtained through symmetry breaking; the remaining 99% is, in fact, the strong force binding energy (remember, mass and energy are equivalent) that holds the quarks together inside protons and neutrons.
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