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Polarization tensor in de Sitter gauge gravity
International Journal of Modern Physics D ( IF 1.8 ) Pub Date : 2021-02-25 , DOI: 10.1142/s0218271821500358 R. Raziani 1 , M. V. Takook 2
International Journal of Modern Physics D ( IF 1.8 ) Pub Date : 2021-02-25 , DOI: 10.1142/s0218271821500358 R. Raziani 1 , M. V. Takook 2
Affiliation
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. 1 0 gauge vector fields are needed which correspond to 1 0 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, 𝒦 α β γ . 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, ℰ α , and tensor polarization of rank-2, ℰ α β , 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:
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。1 0 需要对应的规范向量场1 0 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,𝒦 α β γ . 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,ℰ α ,以及 rank-2 的张量极化,ℰ α β ,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 ) )。
更新日期:2021-02-25
中文翻译:
德西特规范重力中的极化张量
德西特群的规范理论,