Spin and Wave
Function as Attributes of Ideal Fluid
Yuri A. Rylov
An ideal
fluid whose internal energy depends on density, density gradient, and entropy
is considered. Dynamic eqautions are integrated, and a description in terms of
hydrodynamic (Clebsch) potentials arises. All essential information on the
fluid flow (including initial and boundary conditions) appears to be carried by
the dynamic equations for hydrodynamic potentials. Information on initial
values of the fluid flow is carried by arbitrary integration functions. Initial
and boundary conditions for potentials contain only unessential information
concerning the fluid particle labeling. It is shown that a description in terms
of $n$-component complex wave function is a kind of such a description in terms
of hydrodinamic potentials. Spin determined by the irreducible number $n_m$ of the
wave function components appears to be an attribute of the fluid flow. Classification
of fluid flows by the spin appears to be connected with invariant subspaces of
the relabeling group.