  Two critical issues in the study of the fission mechanism are how the fission
fragment angular momenta (FFAM) develop dynamically from equilibrium and how
they are correlated with each other. To this end, we construct a time-dependent
generator coordinate method that incorporates crucial quantum fluctuations --
multiple rotations, vibrations, and their couplings -- based on covariant
density functional theory, providing for the first time a global, microscopic,
and dynamical study on the FFAM distribution. The calculated probability
distributions of FFAM are in good agreement with the experimental measurements,
and the sawtooth-like mass dependence of average FFAM is reproduced very well.
It is noteworthy to find that the quantum fluctuations drive the generation and
chaotic evolution of FFAM during fission fragment formation and induce the
strong correlations of FFAM orientations at the small, medium, and large
opening angles ($\phi_{\rm LH}\approx 30^{\rm o}$, $90^{\rm o}$, $160^{\rm
o}$).
