Spontaneously broken boosts and the Goldstone continuum

Understand

The spontaneous breaking of boost invariance is ubiquitous in nature, yet the associated Goldstone bosons are nowhere to be seen.

• We discuss why some subtleties are to be expected in the Goldstone phenomenon for spontaneously broken boosts, and derive the corresponding quantum mechanical, non-perturbative Goldstone theorem.
• Despite similarities with more standard Goldstone theorems, we show by examples that ours can be obeyed by quite unusual spectra of low-energy excitations.
• In particular, for non-relativistic Fermi liquids, we prove that it is obeyed by the particle-hole continuum.