Broken Symmetries and the Masses of Gauge Bosons

TLDR: In this paper, it was shown that the spin-one quanta of some of the gauge fields acquire mass; the longitudinal degrees of freedom of these particles (which would be absent if their mass were zero) go over into the Goldstone bosons when the coupling tends to zero.

Abstract: In a recent note' it was shown that the Goldstone theorem, ' that Lorentz-covaria. nt field theories in which spontaneous breakdown of symmetry under an internal Lie group occurs contain zero-mass particles, fails if and only if the conserved currents associated with the internal group are coupled to gauge fields. The purpose of the present note is to report that, as a consequence of this coupling, the spin-one quanta of some of the gauge fields acquire mass; the longitudinal degrees of freedom of these particles (which would be absent if their mass were zero) go over into the Goldstone bosons when the coupling tends to zero. This phenomenon is just the relativistic analog of the plasmon phenomenon to which Anderson' has drawn attention: that the scalar zero-mass excitations of a superconducting neutral Fermi gas become longitudinal plasmon modes of finite mass when the gas is charged. The simplest theory which exhibits this behavior is a gauge-invariant version of a model used by Goldstone' himself: Two real' scalar fields y„y, and a real vector field A interact through the Lagrangian density