关于Vierbein的手征替代物的表示
On representations of a chiral alternative to vierbein
摘要：
为了促进引力的量子理论的构建，特胡夫特考虑了广义相对论中的维尔拜因场的手征替代物。这些对象$ f^a{}_{μν}$的行为类似于度量张量的“立方根”。我们试图构建这些张量的狄拉克$γ$矩阵在欧氏空间和闵可夫斯基空间的具体表示，并促进这些弯曲的空间通过彭罗斯-纽曼形式主义。我们推测这些具有物理意义的新物体是Killing-Yano张量的类似物。
英文摘要：
In an attempt to facilitate the construction of a quantum theory of gravity, 't Hooft has considered a chiral alternative to the vierbein field in general theory of relativity. These objects, $ f^a{}_{μν}$, behave like the "cube root" of the metric tensor. We try to construct specific representations of these tensors in terms of Dirac $γ$ matrices in Euclidean and Minkowski space and promote these to curved space through Penrose-Newman formalism. We conjecture that these new objects, with physical significance, are the analog of Killing-Yano tensors.
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