The gauge theory of the de Sitter group, SO(1, 4), in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. 10 gauge vector fields are needed which correspond to 10 generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-2 gauge potentials has been constructed. 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, 𝒦αβγ. This tensor field has been rewritten in terms of 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, ℰα, and tensor polarization of rank-2, ℰαβ, which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, H = 0, one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-2 mixed symmetry rank-3 tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups (SO(2, 4)).

中文翻译：

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德西特规范重力中的极化张量

德西特群的规范理论，所以(1, 4)，在环境空间中，本文已经考虑了形式主义。该方法对构建德西特超共形引力和量子引力具有重要意义。10需要对应的规范向量场10德西特组的发电机。使用规范不变的拉格朗日，得到了这些矢量场的场方程。规范矢量场解决方案被召回。通过使用这些解决方案，自旋2量规电位已经构建。呈现这个张量场有两种可能性：rank-2对称和混合对称等级-3张量场。为了保持保形变换，自旋2场必须由混合对称等级表示 -3张量场，𝒦αβγ. 该张量场已根据广义极化张量场和德西特平面波进行了改写。该广义极化张量场已被计算为矢量极化的组合，ℰα，以及 rank-2 的张量极化，ℰαβ，可用于引力波考虑。这个张量的选择有一定程度的随意性，我们固定它的方式是，在极限内，H = 0，得到闵可夫斯基时空中的极化张量。已经证明，在一些简单的条件下，自旋2混合对称秩3张量场可以通过德西特和共形群的酉不可约表示同时变换（所以(2, 4)）。