The Vierbein Formalism and Energy-Momentum Tensor of Spinors

Details The Vierbein Formalism and Energy-Momentum Tensor of Spinors The Vierbein Formalism and Energy-Momentum Tensor of Spinors

2006-12-18

arxiv.org/abs/gr-qc/0612106v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, no figure

Scientific paper

In order to study the dynamical behavior of the coupling system of the space-time and Fermions, the explicit form of the energy-momentum tensor of the spinors in curved space-time is wanted. The energy-momentum tensor is closely related to the vierbien formalism, which can not be uniquely determined by the metric. This flexibility increases difficulties to derive the equations and easily leads to ambiguous results. In this paper, we define a spinor coefficient tensor $S^{\mu\nu}_{ab}$ and give some explicit relations between vierbien formalism and metric, and then derive the explicit forms of energy-momentum tensor for both the Weyl spinor and the Dirac bispinor.

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