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Often, we say that the low-energy excitations of a quantum system that spontaneously breaks certain symmetries is described by Goldstone bosons. It is also well-known that Fermi liquids and gases are described by quasiparticle modes as low frequency excitations of the Fermi surface.

Question Is there any sense in which the quasiparticles describing the low-energy dynamics of Fermi liquids and gases can be understood as Goldstones (possibly related to the spontaneous symmetry breaking of boosts)?

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  • $\begingroup$ Do you have a specific spontaneously-symmetry breaking Fermi liquid in mind? $\endgroup$
    – SuperCiocia
    Commented Jul 7, 2019 at 10:22
  • $\begingroup$ At a minimum. Fermi liquids must break Lorentz boost symmetry (or in the non-relativistic approximation, Galilean boost symmetry)... not sure if it breaks any others. $\endgroup$
    – user105620
    Commented Jul 7, 2019 at 15:25
  • $\begingroup$ why do Fermi liquids need to break Lorentz boost symmetry? $\endgroup$
    – SuperCiocia
    Commented Jul 7, 2019 at 16:01
  • $\begingroup$ because these is a preferred rest-frame, namely the rest frame of the fermi liquid. In other words, think about a fermi liquid at rest vs one that is boosted to some non-zero velocity... they will be in different states, i.e. boosts are spontaneously broken. $\endgroup$
    – user105620
    Commented Jul 7, 2019 at 18:23

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