Redundancies in Nambu-Goldstone Bosons

Abstract

We propose a simple criterion to identify when Nambu-Goldstone bosons (NGBs) for different symmetries are redundant. It solves an old mystery why crystals have phonons for spontaneously broken translations but no gapless excitations for equally spontaneously broken rotations. Similarly for a superfluid, the NGB for spontaneously broken Galilean symmetry is redundant with phonons. The most nontrivial example is Tkachenko mode for a vortex lattice in a superfluid, where phonons are redundant to the Tkachenko mode which is identified as the Boboliubov mode.

4 pages; discussion improved, new references added

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• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
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