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Prog. Theor. Phys. Vol. 14 No. 4 (1955) pp. 283-302

The Vector Representation of Spinning Particle in the Quantum Theory, I

Takehiko Takabayasi

Physical Institute, Nagoya University, Nagoya

(Received July 22, 1955)

Abstract:

A quantum-mechanical non-relativistic spinnig particle is represented equivalently with a non-linear vector field which defines a new kind of hydrodynamics of a spinning fluid. In this hydrodynamics, quantum effects are separated as non-linear terms which mean the occurrence of “internal potential” and “internal magnetic field”.
Mathematically, the method is based upon the replacement of the original calculus in terms of a spinor ψ by the calculus in terms of tensors formed as the bilinear expressions in ψ^* and ψ. This replacement is ensured by setting up the identities which should hold among those tensor quantities.

URL : http://ptp.ipap.jp/link?PTP/14/283/
DOI : 10.1143/PTP.14.283

[ Full Text PDF : FREE ACCESS (1477K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. T. Takabayasi, Prog. Theor. Phys. 8 (1952), 143[PTP]; ibid. 9 (1953), 187[PTP].
2. D. Bohm and J. P. Vigier, Phys. Rev. 96 (1954), 208[APS].
   M. Schönberg, Nuovo Cim. 12 (1954), 103; ibid. 12 (1954), 649.
3. cf. W. Pauli, Helv. Phys. Acta 12 (1939), 147.
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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 18 No. 6 (1957) pp. 573-590 :

   Description of Pauli Matter as a Continuous Assembly of Small Rotating Bodies

   Takehiko Takabayasi and Jean-Pierre Vigier

2. Progress of Theoretical Physics Vol. 36 No. 1 (1966) pp. 72-85 :

   A New Derivation of Classical Models of the Spinning Electron from the WKB Solutions to the Pauli and Dirac Equations

   Hisaiti Yamasaki

3. Progress of Theoretical Physics Vol. 43 No. 4 (1970) pp. 861-869 :

   Formulation of the Uncertainty Principle According to the Hydrodynamic Model of Quantum Mechanics

   H. E. Wilhelm

4. Progress of Theoretical Physics Vol. 69 No. 5 (1983) pp. 1323-1344 :

   Hydrodynamical Formalism of Quantum Mechanics and Aharonov-Bohm Effect

   Takehiko Takabayasi

5. Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 1-17 :

   Vortex, Spin and Triad for Quantum Mechanics of Spinning Particle.I

   Takehiko Takabayasi

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