  We introduce the perturbative $\hbar$-power series ($\hbar$ = Planck
constant) providing the algebraic solutions of $D=4$ quantum Snyder and Yang
models which describe relativistic quantum space-times and Lorentz-covariant
quantum phase spaces. We argue that if in these series the zero order ($\hbar
$-independent) terms are non-vanishing they describe the spontaneous symmetry
breaking (SSB) parameters of Lie-algebraic symmetries which characterize the
considered models ($D=4$ dS symmetry in Snyder and $D=5$ dS symmetry in Yang
cases). The consecutive terms in $\hbar$-power series can be calculated
explicitly if we supplement the SSB order parameters (Nambu-Goldstone or NG
modes) by dual set of commutative momenta, which together define the canonical
tensorial Heisenberg algebra.
