Vortex, Spin and Triad for Quantum Mechanics of Spinning Particle. Part 1. General Theory

Takabayasi, Takehiko

doi:10.1143/PTP.70.1

Vortex, Spin and Triad for Quantum Mechanics of Spinning Particle. Part 1. General Theory

Takehiko Takabayasi
(
- Nagoya U.
)

Mar, 1983

31 pages

Published in:

Prog.Theor.Phys. 70 (1983) 1

Contribution to:

11th International Symposium on Lepton and Photon Interactions at High Energies

DOI:

10.1143/PTP.70.1

Report number:

DPNU-03-83

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Abstract: (Oxford Journals)

It is shown that a natural extension of the hydrodynamical formalism of quantum mechanics for a Schrödinger particle to include vortical flows leads to the hydrodynamical formalism of quantum mechanics for a spinning particle. This latter formalism is then analysed in regard to its characteristic features, especially the subsidiary condition connecting the vorticity of flow with the inhomogeneity of spin field and the existence of spin stress. Also the formalism is brought to completion by establishing the global condition that quantizes circulation around a singular vortex line. The geometro-hydrodynamical formalism which is equivalent to the above hydrodynamical formalism but introduces a triad structure underlying the classical spin is reconstructed on its own footing. The geometrical property of the triad implies the invariance of theory with respect to the rotation of each triad around its symmetry axis by an arbitrary angle, and this necessitates the introduction of the electromagnetic potential, providing the geometrical interpretation of local gauge invariance. Applications of theory to various special cases and typical examples are deferred to Part II.

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