  Although highly successful, the Truncated Wigner Approximation (TWA) does not
account for genuine many-body quantum interference between different solutions
of the mean-field equations of a bosonic many-body (MB) system. This renders
the TWA essentially classical, where a large number of particles formally takes
the role of the inverse of Planck's constant $\hbar$. The failure to describe
genuine interference phenomena, such as localization and scarring in Fock
space, can be seen as a virtue of this quasiclassical method, which thereby
allows one to identify genuine quantum effects when being compared with "exact"
quantum calculations that do not involve any a priori approximation. A rather
prominent cause for such quantum effects that are not accounted for by the TWA
is the constructive interference between the contributions of symmetry-related
trajectories, which would occur in the presence of discrete symmetries provided
the phase-space distribution of the initial state and the observable to be
evaluated feature a strong localization about the corresponding symmetry
subspaces. Here we show how one can conceive an augmented version of the TWA
which can account for this particular effect. This augmented TWA effectively
amounts to complementing conventional TWA calculations by separate Truncated
Wigner simulations that are restricted to symmetric subspaces and involve
weight factors that account for the dynamical stability of sampling
trajectories with respect to perpendicular deviations from those subspaces. We
illustrate the validity of this method at pre- as well as post-Ehrenfest time
scales in prototypical Bose-Hubbard systems displaying chaotic classical
dynamics, where it also reveals the existence of additional MB interference
effects.
