  We present a Bayesian phase-space reconstruction of the cosmic large-scale
matter density and velocity fields from the SDSS-III Baryon Oscillations
Spectroscopic Survey Data Release 12 (BOSS DR12) CMASS galaxy clustering
catalogue. We rely on a given $\Lambda$CDM cosmology, a mesh resolution in the
range of 6-10 $h^{-1}$ Mpc, and a lognormal-Poisson model with a redshift
dependent nonlinear bias. The bias parameters are derived from the data and a
general renormalised perturbation theory approach. We use combined Gibbs and
Hamiltonian sampling, implemented in the \textsc{argo} code, to iteratively
reconstruct the dark matter density field and the coherent peculiar velocities
of individual galaxies, correcting hereby for coherent redshift space
distortions (RSD). Our tests relying on accurate $N$-body based mock galaxy
catalogues, show unbiased real space power spectra of the nonlinear density
field up to $k\sim0.2\, h$ Mpc$^{-1}$, and vanishing quadrupoles down to
$r\sim20\,h^{-1}$ Mpc. We also demonstrate that the nonlinear cosmic web can be
obtained from the tidal field tensor based on the Gaussian component of the
reconstructed density field. We find that the reconstructed velocities have a
statistical correlation coefficient compared to the true velocities of each
individual lightcone mock galaxy of $r\sim0.68$ including about 10% of
satellite galaxies with virial motions (about $r=0.75$ without satellites). The
power spectra of the velocity divergence agree well with theoretical
predictions up to $k\sim0.2\,h\,{\rm Mpc}^{-1}$. This work will be especially
useful to improve, e.g. BAO reconstructions, kinematic Sunyaev-Zeldovich (kSZ),
integrated Sachs-Wolfe (ISW) measurements, or environmental studies.
