Soft theorems for boosts and other time symmetries

Understand

We derive soft theorems for theories in which time symmetries -- symmetries that involve the transformation of time, an example of which are Lorentz boosts -- are spontaneously broken.

• The soft theorems involve unequal-time correlation functions with the insertion of a soft Goldstone in the far past.
• Explicit checks are provided for several examples, including the effective theory of a relativistic superfluid and the effective field theory of inflation.
• We discuss how in certain cases these unequal-time identities capture information at the level of observables that cannot be seen purely in terms of equal-time correlators of the field alone.