Some applications of a Lorentz-like formulation of Galilean invariance
Abstract:
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.