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.
CITATION STYLE
Hehl, F. W., Macías, A., Mielke, E. W., & Obukhov, Y. N. (1999). On the Structure of the Energy-Momentum and the Spin Currents in Dirac’s Electron Theory. In On Einstein’s Path (pp. 257–274). Springer New York. https://doi.org/10.1007/978-1-4612-1422-9_18
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