= Higgs mechanism
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In the Higgs mechanism, gauge fields associated with broken generators acquire longitudinal polarizations and masses by absorbing Goldstone modes. Gauge fields of the unbroken subgroup remain massless.
The phrase “absorbing” describes a rearrangement of <degrees of freedom>, not a collision in which a <gauge boson> swallows another particle. The <gauge symmetry> remains a redundancy of the description. A chosen <vacuum expectation value> leaves a smaller subgroup manifest, while <gauge-invariant> observables describe the physical masses.
A one-field calculation isolates the mechanism. In an <Abelian Higgs model>, write a complex <scalar field> locally as $\Phi=(v+H)e^{i\theta}/\sqrt2$, use $D_\mu=\partial_\mu-ieA_\mu$, and define $B_\mu=A_\mu-\partial_\mu\theta/e$. Then
$$
|D_\mu\Phi|^2=\frac12(\partial_\mu H)^2+\frac12e^2(v+H)^2B_\mu B^\mu.
$$
The second term contains a <Proca field> mass $m_B=ev$ and its interactions with the radial <Higgs boson>. A local <gauge transformation> removes $\theta$ from the <scalar field> but leaves its information in the longitudinal vector polarization. The <electroweak symmetry breaking> calculation applies this idea to three broken directions.
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