标题： Witten旋量哈密顿表述能否描述广义相对论的角动量？ 显示英文标题

标题： Can Witten spinor Hamiltonian formulation describe the GR angular momentum?

摘要： Witten旋量哈密顿形式之前已被证明能够为GR能量动量提供一种准局部化，这导致了当旋量满足Witten方程时正能的证明。 在本工作中，我们研究这种形式是否也能描述GR角动量。 我们基于Witten方案设想了四个二次旋量哈密顿量作为角动量的候选。 第一个是通过将旋量伪矢量参数化替换为位移的旋量矢量参数化而在Witten哈密顿量中获得的。 其他三个各自由其他二次旋量项组成，所有这些都包含由反对称二阶张量的旋量参数化和位置矢量组成的位移，其中一个有4项，其他每个都有两两不同的2项。 在平坦时空周围的可能场扰动下，我们发现这四个候选都无法给出角动量的准局部化。 讨论了成功地将角动量包括在Witten形式中的重要性和前景。 显示英文摘要

摘要： The Witten spinor Hamiltonian formulation has previously been shown to be able to yield a quasilocalization for the GR energy-momentum which leads to a proof of the positive energy when the spinor satisfies the Witten equation. In this work we investigate whether this formulation can also describe the GR angular momentum. We conceive four candidates of the quadratic spinor Hamiltonian for the angular momentum based on Witten's scheme. The first one is acquired by substituting the spinor pseudovectorial parameterization for the spinor vectorial parameterization of the displacement in the Witten Hamiltonian. The other three each are composed of other quadratic spinor terms, all with the displacement consisting of the spinor parameterization of an antisymmetric 2-rank tensor and a position vector, one having 4 terms and the others each having twice distinct 2 of the 4 terms. With possible field perturbations around the at spacetime we find none of the four candidates can give the angular momentum quasilocalization. The importance and prospects for successfully including the angular momentum in Witten's formalism are discussed.