One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited for a hydrodynamical reformulation of the BZ theory. Working out a “probabilistic fluid,” we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to “quantize” the BZ theory: by employing this time the tensorial language, more popular in first-quantization. “Quantizing” the BZ theory, however, does notlead to the Dirac equation, but rather to a nonlinear, Dirac–like equation, which can be regarded as the actual “quantum limit” of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical “Weyssenhoff fluid,” while the Hamilton-Jacobi equation (linking mass, spin,and zbw frequency together) appears to be nothing but a special case of the de Broglie energy–frequency relation. Finally, after having discussed the remarkable relation existing between the gauge transformation U(1) and ageneral rotation on the spin plane, we clarify and comment on the two-valuedeness nature of the fremionic wave-function, as well as on the parity and charge conjugation transformations.

(1997). Hydrodynamical Reformulation and Quantum Limit of the Barut-Zanghi Theory [journal article - articolo]. In FOUNDATIONS OF PHYSICS LETTERS. Retrieved from http://hdl.handle.net/10446/125052

Hydrodynamical Reformulation and Quantum Limit of the Barut-Zanghi Theory

Salesi, Giovanni
1997-01-01

Abstract

One of the most satisfactory pictures for spinning particles is the Barut-Zanghi (BZ) classical theory for the relativistic extended-like electron, that relates spin to zitterbewegung (zbw). The BZ motion equations constituted the starting point for recent works about spin and electron structure, co-authored by us, which adopted the Clifford algebra language. This language results to be actually suited for a hydrodynamical reformulation of the BZ theory. Working out a “probabilistic fluid,” we are allowed to reinterpret the original classical spinors as quantum wave-functions for the electron. We can pass to “quantize” the BZ theory: by employing this time the tensorial language, more popular in first-quantization. “Quantizing” the BZ theory, however, does notlead to the Dirac equation, but rather to a nonlinear, Dirac–like equation, which can be regarded as the actual “quantum limit” of the BZ classical theory. Moreover, a new variational approach to the BZ probabilistic fluid shows that it is a typical “Weyssenhoff fluid,” while the Hamilton-Jacobi equation (linking mass, spin,and zbw frequency together) appears to be nothing but a special case of the de Broglie energy–frequency relation. Finally, after having discussed the remarkable relation existing between the gauge transformation U(1) and ageneral rotation on the spin plane, we clarify and comment on the two-valuedeness nature of the fremionic wave-function, as well as on the parity and charge conjugation transformations.
articolo
1997
Recami, Erasmo; Salesi, Giovanni
(1997). Hydrodynamical Reformulation and Quantum Limit of the Barut-Zanghi Theory [journal article - articolo]. In FOUNDATIONS OF PHYSICS LETTERS. Retrieved from http://hdl.handle.net/10446/125052
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