Quantum scale invariant gravity in the de Donder gauge
Quantum scale invariant gravity in the de Donder gauge
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DOI：
10.1103/physrevd.105.066001
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发表时间：
2022-01
影响因子：
5
通讯作者：
I. Oda
中科院分区：
文献类型：
--
作者：
I. Oda
在一般坐标不变性的de Donder规范条件（或调和规范条件）下，利用标量场对标度不变引力进行了显协变量子化，通过标量场的场重定义，将标度不变引力等价于著名的Brans-Dicke引力.首先，在不指定引力理论的表达式的情况下，我们写出各种等时（反）对易关系（ETCR），特别是仅基于de Donder规范条件的涉及Nakanishi-Lautrup场、FP鬼和FP反鬼的ETCR。结果表明，它是一种Poincaré型的IOSp（8| 8）超对称性，可以从这样一个一般的作用与德唐德规范。其次，以标量场的标度不变引力为经典理论，导出了包含度规张量和标量场的引力扇区的ETCR。此外，我们解释了尺度对称性是如何在量子引力中自发破缺的，从而证明了量子子是一个无质量的南武-戈德斯通粒子。电子邮件地址：ioda@sci.u-ryukyu.ac.jp
We perform the manifestly covariant quantization of a scale invariant gravity with a scalar field, which is equivalent to the well-known Brans-Dicke gravity via a field redefinition of the scalar field, in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. First, without specifying the expression of a gravitational theory, we write down various equal-time (anti-)commutation relations (ETCRs), in particular, those involving the Nakanishi-Lautrup field, the FP ghost, and the FP antighost only on the basis of the de Donder gauge condition. It is shown that choral symmetry, which is a Poincaré-like IOSp(8|8) supersymmetry, can be derived from such a general action with the de Donder gauge. Next, taking the scale invariant gravity with a scalar field as a classical theory, we derive the ETCRs for the gravitational sector involving the metric tensor and scalar fields. Moreover, we account for how scale symmetry is spontaneously broken in quantum gravity, thereby showing that the dilaton is a massless Nambu-Goldstone particle. E-mail address: ioda@sci.u-ryukyu.ac.jp