Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-06-03
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, latex2e, no figures, to appear in: "On Einstein's Path". Festschrift for E. Schucking on the occasion of his 70th bi
Scientific paper
We consider a classical Dirac field in flat Minkowski spacetime. We perform a Gordon decomposition of its canonical energy-momentum and spin currents, respectively. Thereby we find for each of these currents a convective and a polarization piece. The polarization pieces can be expressed as exterior covariant derivatives of the two-forms $\check M_\alpha$ and $M_{\alpha\beta}=-M_{\beta\alpha}$, respectively. In analogy to the magnetic moment in electrodynamics, we identify these two-forms as gravitational moments connected with the translation group and the Lorentz group, respectively. We point out the relation between the Gordon decomposition of the energy-momentum current and its Belinfante-Rosenfeld symmetrization. In the non-relativistic limit, the translational gravitational moment of the Dirac field is found to be proportional to the spin covector of the electron.
Hehl Friedrich W.
Macias Alfredo
Obukhov Yu N.
~Mielke Eckehard W.
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