How the Higgs mechanism works — spontaneous breaking of electroweak symmetry gives W and Z bosons their mass

What spontaneous symmetry breaking does — the vacuum state breaks a symmetry that the laws possess

Vacuum state in quantum field theory breaks global U(1) gauge symmetry

What the Higgs field does — permeates all space, gives mass to fundamental particles through coupling

The Higgs field permeates space, endowing particles with mass via interaction

What the Goldstone theorem says — every spontaneously broken continuous symmetry produces a massless boson

Goldstone theorem: Spontaneously broken continuous symmetries yield massless Goldstone bosons

What the electroweak unification achieved — Glashow, Salam, and Weinberg showed EM and weak force are one

Unified electroweak theory: EM and weak force as one interaction

Which gauge symmetry underlies the unification of the electromagnetic, weak, and strong forces at high energies, and how does it manifest in the Standard Model?

SU(2)xSU(3) gauge symmetry unifies forces in the Standard Model, manifesting as weak and strong interactions

What gauge symmetry is — local phase transformations that leave physics invariant, the basis of all fundamental forces

Gauge symmetry: Local phase transformations preserving physics, underlying fundamental forces