  The family of trajectories-based approximations employed in computational
quantum physics and chemistry is very diverse. For instance, Bohmian and
Heller's frozen Gaussian semiclassical trajectories seem to have nothing in
common. Based on a hydrodynamic analogy to quantum mechanics, we furnish the
unified gauge theory of all such models. In the light of this theory, currently
known methods are just a tip of the iceberg, and there exists an infinite
family of yet unexplored trajectory-based approaches. Specifically, we show
that each definition for a semiclassical trajectory corresponds to a specific
hydrodynamic analogy, where a quantum system is mapped to an effective
probability fluid in the phase space. We derive the continuity equation for the
effective fluid representing dynamics of an arbitrary open bosonic many-body
system. We show that unlike in conventional fluid, the flux of the effective
fluid is defined up to Skodje's gauge [R. T. Skodje et. al. Phys. Rev. A 40,
2894 (1989)]. We prove that the Wigner, Husimi and Bohmian representations of
quantum mechanics are particular cases of our generic hydrodynamic analogy, and
all the differences among them reduce to the gauge choice. Infinitely many
gauges are possible, each leading to a distinct quantum hydrodynamic analogy
and a definition for semiclassical trajectories. We propose a scheme for
identifying practically useful gauges and apply it to improve a semiclassical
initial value representation employed in quantum many-body simulations.
