  A constructive theoretical platform for the description of quantum space-time
crystals uncovers for $N$ interacting and ring-confined rotating particles the
existence of low-lying states with proper space-time crystal behavior. The
construction of the corresponding many-body trial wave functions proceeds first
via symmetry breaking at the mean-field level followed by symmetry restoration
using projection techniques. The ensuing correlated many-body wave functions
are stationary states and preserve the rotational symmetries, and at the same
time they reflect the point-group symmetries of the mean-field crystals. This
behavior results in the emergence of sequences of select magic angular momenta
$L_m$. For angular-momenta away from the magic values, the trial functions
vanish. Symmetry breaking beyond mean field can be induced by superpositions of
such good-$L_m$ many-body stationary states. We show that superposing a pair of
adjacent magic angular momenta states leads to formation of special
broken-symmetry states exhibiting quantum space-time-crystal behavior. In
particular, the corresponding particle densities rotate around the ring,
showing undamped and nondispersed periodic crystalline evolution in both space
and time. The experimental synthesis of such quantum space-time-crystal wave
packets is predicted to be favored in the vicinity of ground-state energy
crossings of the Aharonov-Bohm-type spectra accessed via an externally applied
magnetic field. These results are illustrated here for Coulomb-repelling
fermionic ions and for a lump of contact-interaction attracting bosons.
