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arXiv 0905.4529gr-qchep-thmath-phmath.MP
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渐近平坦时空的内自旋Angular Momentum

The Internal Spin Angular Momentum of an Asymptotically Flat Spacetime

Andrew Randono, David Sloan

摘要:

本文研究了在渐近无穷远处的引力场中旋量场的内自旋角动量的编码方式。内旋的加入要求我们重新分析渐近平坦性的概念。特别是,在渐近无穷远处的庞加莱对称性必须被自旋扩大的庞加莱对称性所取代。同样地,渐近对称群的生成元必须被补充以解释内自旋。在一阶Einstein-Cartan引力的Hamilton框架中,额外生成元来自于渐近平坦背景下高斯约束的边界项。通过引入附加项,我们建立了Dirac场的Noether荷、Komar积分和渐近类ADM几何积分之间的关系。我们表明,通过施加温和的限制规范变换的生成泛函在渐近无穷远,相空间呈现显式有限。我们构造的能量动量和新的总(自旋+轨道)角动量边界积分,满足适当的代数是自旋扩大庞加莱对称的发电机。这表明内自旋在渐近无穷远处被编码在四分体中。此外,我们发现,一个新的保守和(自旋放大)庞加莱不变的费用出现,是与全球结构的规范变换。

英文摘要:

In this paper we investigate the manner in which the internal spin angular momentum of a spinor field is encoded in the gravitational field at asymptotic infinity. The inclusion of internal spin requires us to re-analyze our notion of asymptotic flatness. In particular, the Poincaré symmetry at asymptotic infinity must replaced by a spin-enlarged Poincaré symmetry. Likewise, the generators of the asymptotic symmetry group must be supplemented to account for the internal spin. In the Hamiltonian framework of first order Einstein-Cartan gravity, the extra generator comes from the boundary term of the Gauss constraint in the asymptotically flat context. With the additional term, we establish the relations among the Noether charges of a Dirac field, the Komar integral, and the asymptotic ADM-like geometric integral. We show that by imposing mild restraints on the generating functionals of gauge transformations at asymptotic infinity, the phase space is rendered explicitly finite. We construct the energy-momentum and the new total (spin+orbital) angular momentum boundary integrals that satisfy the appropriate algebra to be the generators of the spin-enlarged Poincaré symmetry. This demonstrates that the internal spin is encoded in the tetrad at asymptotic infinity. In addition, we find that a new conserved and (spin-enlarged) Poincaré invariant charge emerges that is associated with the global structure of a gauge transformation.

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