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

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

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

Higgs field's non-zero vacuum expectation value breaks symmetry, endowing W and Z bosons with mass

What does Noether's theorem state about the relationship between continuous symmetries and conservation laws in physics?

Noether's theorem links each continuous symmetry to a corresponding conservation law

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

What CPT symmetry is — the combination of charge, parity, and time reversal is always conserved

CP-symmetry implies charge, parity, and time reversal conservation

What the strong CP problem is — why does QCD not violate CP symmetry when it has no reason not to

The strong CP problem questions why CP violation isn't observed in Quantum Chromodynamics despite theoretical possibility