Goldstone boson: Difference between revisions

== Nonrelativistic theories ==
A version of Goldstone's theorem also applies to [[nonrelativistic]] theories (and also relativistic theories with spontaneously broken [[Lorentz symmetry]]). It basically states that for each spontaneously broken global symmetry, there corresponds a [[quasiparticle]] with no [[energy gap]] (the nonrelativistic version of the [[mass gap]]). It's important to note that the energy here is really <math>H-\mu N-\vec{\alpha}\cdot\vec{P}</math> and not <math>H</math>. However, two different spontaneously broken generators may give rise to the same Goldstone boson. For example, in a [[superfluid]], both the [[U(1)]] particle number symmetry and [[Galilean symmetry]] are spontaneously broken. However, the [[phonon]] is the Goldstone boson for both.
In fact, in general, the phonon is the Goldstone boson for spontaneously broken [[Galilean]]/Lorentz symmetry.