Quadratic gravity and restricted Weyl symmetry
Quadratic gravity and restricted Weyl symmetry
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DOI：
10.1142/s021773232150139x
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
A. Kamimura;I. Oda
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作者：
A. Kamimura;I. Oda
在弯曲时空中，研究了二次引力与Weyl变换的规范参数Ω（x）满足约束条件<$Ω = 0的限制Weyl对称性之间的关系.首先，我们简要回顾了在平坦Minkowski时空中U（1）规范参数θ（x）服从类似的约束条件θ θ = 0的QED模型，并解释了约束规范对称性去除了规范场的一个壳层模，它与Feynman规范一起只留下两个横极化作为物理状态。接下来，它表明，限制外尔对称性也消除了偶极场的一个组成部分，在平方重力周围的平坦闵可夫斯基背景，只留下一个单一的标量状态。最后，我们表明，限制外尔对称性不能删除任何动力学自由度的静态背景度规使用二次引力的零能量定理。这一事实也适用于不施加静态条件的欧几里得背景度量。E-mail地址：k208328@eve.u-ryukyu.ac.jp E-mail地址：ioda@sci.u-ryukyu.ac.jp
We investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter Ω(x) of Weyl transformation satisfies a constraint ✷Ω = 0 in a curved space-time. First, we briefly review a model with a restricted gauge symmetry on the basis of QED where a U(1) gauge parameter θ(x) obeys a similar constraint ✷θ = 0 in a flat Minkowski space-time, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition. E-mail address: k208328@eve.u-ryukyu.ac.jp E-mail address: ioda@sci.u-ryukyu.ac.jp