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arXiv 1802.01097hep-thgr-qc
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再论量子引力中的Weinberg No Go定理

More on Weinberg's No Go Theorem in Quantum Gravity

Munehiro Nagahama, Ichiro Oda

摘要:

我们补充温伯格的不去定理的宇宙学常数问题的量子引力推广到一个标度不变的理论。我们的分析利用了显协变量子引力中的有效作用量和BRST对称性,而不是经典引力中的经典拉格朗日密度和$GL(4)$对称性。从这个意义上说,我们的证明是非常一般的,因为它不依赖于量子引力的细节,并且对在量子态射下不变的一般引力理论也成立。作为我们的定理的应用,我们评论的想法,在渐近安全的情况下的功能重整化流驱动器的宇宙学常数为零,解决宇宙学常数的问题,而不参考微调的参数。最后,我们还讨论了将量子引力中的温伯格定理推广到平移不变性自发破缺的可能性。

英文摘要:

We complement Weinberg's no go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the $GL(4)$ symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

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