Dirac Electron in Space-times With Torsion: Spinor Propagation, Spin Precession, and Nongeodesic Orbits
19818 pages
Published in:
- Phys.Rev.D 24 (1981) 1470-1477
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Abstract: (APS)
The WKB limit of the noniterated Dirac equation in a Riemann-Cartan space-time is discussed. It is shown that within this framework the behavior of a Dirac particle is dominated by the new connection Γμν*λ={λ}{μν}−3K[μνε]gελ formed from the Christoffel connection and the contortion. The relevant effects are the following: (i) The normalized Dirac spinor is parallel propagated by Γμν*λ along the particle's orbit. (ii) The same is true for the spin vector. By this the gyrogravitational ratio is specified as well. (iii) The particle orbit is nongeodesic. The respective "force" is of the usual form with the spin coupled to the curvature tensor R*αβγδ(Γ*) of the connection Γμν*λ. The orbit is thereby defined by the streamlines of the conserved convection four-current obtained from the Dirac current by a Gordon decomposition. The cumulative effects (ii) and (iii) can in principle be used to detect torsion by measuring the spin precession of a massive spin-½ particle or by measuring its orbit in a Stern-Gerlach type of experiment.- general relativity
- GRAVITATION
- QUANTUM MECHANICS
- FIELD THEORY: SPACE-TIME
- Dirac equation
- FIELD THEORY: SPINOR
- SPINOR: FIELD THEORY
- SPIN: 1/2
- 1/2: SPIN
- MATHEMATICAL METHODS: DIFFERENTIAL GEOMETRY
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