HYDRODYNAMICAL REFORMULATION AND QUANTUM LIMIT OF THE BARUT-ZANGHI-THEORY

One of the most satisfactory pictures for spinning particles is the Ba rut-Zanghi (BZ) classical theory for the relativistic extended-like el ectron, that relates spin to zitterbewegung (zbw). The BZ motion equat ions constituted the starting point for recent works about spin and el ectron structure, co-authored by us, which adopted the Clifford algebr a language. This language results to be actually suited for a hydrodyn amical reformulation of the BZ theory. Working out a ''probabilistic f luid,'' we are allowed to reinterpret the original classical spinors a s quantum wave-functions for the electron. We can pass to ''quantize'' the BZ theory: by employing this time the tensorial language, more po pular in first-quantization. ''Quantizing'' the BZ theory, however, do es not lead to the Dirac equation, but rather to a nonlinear, Dirac-li ke equation, which can be regarded as the actual ''quantum limit'' of the BZ classical theory. Moreover, a new variational approach to the B Z probabilistic fluid shows that it is a typical ''Weyssenhoff fluid,' ' while the Hamilton Jacobi equation (linking mass, spin, and zbw freq uency together) appears to be nothing but a special case of the de Bro glie energy-frequency relation. Finally, after having discussed the re markable relation existing between the gauge transformation U(1) and a general rotation on the spin plane, we clarify and comment on the two -valuedness nature of the fermionic wave-function, as well as on the p arity and charge conjugation transformations.