In section 19.6 of Weinberg Vol II, there is a discussion of the coset construction for effective actions of Goldstones arising from spontaneous symmetry breaking of internal symmetries. In this section, he breaks up the fields of the high energy theory, $\psi$, into Goldstone and non-Goldstone pieces by $$\psi(x) = \gamma(x)\cdot \tilde\psi(x), $$ where $\gamma(x)$ are local symmetry transformations parameterized by the Goldstone fields and $\tilde\psi(x)$ contain no Goldstones. To ensure that $\tilde\psi$ contains no Goldstones, Weinberg imposes the constraint equation $$\tilde\psi(x) \cdot t^\alpha \cdot\langle\psi\rangle=0 .$$
Question: Is there an analogous procedure for dealing with situations in which spacetime symmetries are broken as well? More specifically, if spacetime symmetries are broken, what constraints can we impose on $\tilde\psi$ to ensure it contains no Goldstones?
