论文标题
de Sitter量规重力中的极化张量
Polarization tensor in de Sitter gauge gravity
论文作者
论文摘要
本文考虑了Sitter组的仪表理论，因此在环境空间形式主义中$（1,4）$。该方法对于构建保姆超符号重力和量子重力至关重要。需要$ 10 $量规矢量字段，对应于Sitter Group的$ 10 $发电机。使用规格不变的拉格朗日，已经获得了这些向量场的场方程。召回量规矢量场解决方案。然后，从量规矢量场构建了旋转$ 2 $量规的电势。展示此张量字段有两种可能性：排名 - $ 2 $对称和混合对称排名-3 $ tensor字段。为了保留共形转换，必须由混合对称等级来表示旋转$ 2 $的场 - $ 3 $ tensor场，$ \ Mathcal {k} _ {αβγ} $。该张量场已使用广义极化张量场和DE Sitter平面波改写。该广义极化张量场已被计算为向量极化，$ \ MATHCAL {E}_α$的组合以及等级的张量极化 - $ 2 $，$ \ MATHCAL {E} _ {αβ} $，可用于雷神波动的考虑。为了构建这种极化张量，出现任意恒定矢量场。我们对其进行修复，以便在限制中$ h = 0 $，在Minkowski时空获得了极化张量。已经表明，在某些简单的条件下，$ 2 $混合对称排名-3 $张量球场可以与De Sitter和Sonformal群体的单一不可减至的代表同时转换，因此$（2,4）$。
The gauge theory of the de Sitter group, SO$(1,4)$, in the ambient space formalism has been considered in this article. This method is essential to constructing the de Sitter super-conformal gravity and Quantum gravity. $10$ gauge vector fields are needed, corresponding to $10$ generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equation of these vector fields has been obtained. The gauge vector field solutions are recalled. Then, the spin-$2$ gauge potentials are constructed from the gauge vector field. There are two possibilities for presenting this tensor field: rank-$2$ symmetric and mixed symmetry rank-$3$ tensor fields. To preserve the conformal transformation, a spin-$2$ field must be represented by a mixed symmetry rank-$3$ tensor field, $\mathcal {K}_{αβγ}$. This tensor field has been rewritten using a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, $\mathcal {E}_α$, and tensor polarization of rank-$2$, $\mathcal {E}_{αβ}$, which can be used in the gravitational wave consideration. For the construction of this polarization tensor, the arbitrary constant vector fields appear. We fix it so that, in the limit, $H=0$, one obtains the polarization tensor in Minkowski space-time. It has been shown that under some simple conditions, the spin-$2$ mixed symmetry rank-$3$ tensor field can be simultaneously transformed by the unitary irreducible representation of de Sitter and conformal groups, SO$(2,4)$.
