Is THIS what the Higgs boson is?

There's tons of questions on here asking what the Higgs boson is. I haven't seen a very adequate answer. I think I have a vague grasp of it, but I need confirmation.

The important thing is first the Higgs field. The Higgs field interacts with certain particles. In a similar way to how being in an electric field gives an electron potential energy, being in the Higgs field gives any particle that interacts with it potential energy.

Energy IS mass. By having Higgs potential energy, the particle has some energy that is not associated with its momentum, p.

E > pc

E^2 > p^2 c^2

E^2 = p^2 c^2 + X

The full relativistic energy-momentum equation is

E^2 = p^2 c^2 + m0^2 c^4

So

X = m0^2 c^4

X > 0

m0 =/= 0

The particle has invariant mass a.k.a. rest mass.

Also,

v = pc^2 / E

= (pc / E)c

pc < E so

v < c

The particle travels at less than light speed.

So that's generally how the Higgs field results in some particles having mass. Quantum theory says that every field has to have a particle. For example, the electric field is associated with the particle, the photon. The particle for the Higgs field is the Higgs boson.

In an atom, there is an electric field holding the electrons close to the protons on the nucleus. There are photons associated with that electric field, but they're virtual photons. Analogously, particles that have mass are associated with a Higgs field and Higgs bosons, but they're virtual Higgs bosons.

Given the right energy, an atom can emit a real photon. Likewise, a particle can emit a real Higgs boson, but it requires much more energy than a photon.

Is that the gist of it?