Spin and Wave Function as Attributes of Ideal Fluid

Abstract

An ideal fluid whose the internal energy depends on density, gradient density and entropy is considered. Dynamic eqautions are integrated, and a description in terms of hydrodynamic (Clebsch) potentials arises. Integration of hydrodynamic equations generates an arbitrary vector g in the 3-dimensional space of Lagrangian coordinates (particle labels). This vector field g can be expressed via boundary and initial conditions. All essential information on the fluid flow (including initial and boundary conditions) appears to be carried by the dynamic equations for hydrodynamic potentials in the form of arbitrary integration functions g. Initial and boundary conditions for potentials carry only unessential information concerning the fluid particle labeling. They may be chosen in an universal form. It is shown that a description in terms of n-component complex wave function is a kind of a description in terms of hydrodinamic potentials. Spin determined by the irreducible number n of the wave function components appears to be an attribute of the fluid flow. Classification of fluid flows over the spin is connected with invariant subspaces of the relabeling group.