Note on scalars, perfect fluids, constrained field theories, and all that

The relation of a scalar field with a perfect fluid has generated some debate along the last few years. In this Letter we argue that shift-invariant scalar fields can describe accurately the potential flow of an isentropic perfect fluid, but, in general, the identification is possible only for a finite period of time. After that period in the evolution the dynamics of the scalar field and the perfect fluid branch off. The Lagrangian density for the velocity-potential can be read directly from the expression relating the pressure with the Taub charge and the entropy per particle in the fluid, whereas the other quantities of interest can be obtained from the thermodynamic relations.