Spin and Wave Function as Attributes of Ideal Fluid

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences,
101, bld.1 Vernadskii Ave. , Moscow, 117526, Russia.
e-mail: rylov@ipmnet.ru


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.

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