Some applications of a Lorentz-like formulation of Galilean invariance
I describe and illustrate a 4+1 metric formulation of Galilean covariance. It provides a guide for constructing -and eventually solving- non-relativistic equations of many-body theory, analogous to Lorentz-covariance in the relativistic regime. After considering briefly the Galilean versions of Maxwell, Dirac and Bhabha equations, I turn to various hydrodynamical models. I use the formalism to retrieve the Euler equations, the Chaplygin gas model and liquid helium models: irrotational barotropic fluids, non-barotropic fluids and the Thellung-Ziman model for helium II.