Within the background field formalism of quantum gravity, I show that if the quantum fluctuations are limited to diffeomorphic gauge transformations rather than the physical degrees of freedom, as in conventional quantum field theory, all the quantum corrections vanish on shell and the effective action is equivalent to the classical action. In principle, the resulting theory is finite and unitary, and requires no renormalization. I also show that this is the unique parameterization that renders the path integral independent of the on-shell condition for the background field, a form of background independence. Thus, a connection is established between background independence and renormalizability and unitarity.

中文翻译：

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将量子引力的涨落限制为微分同胚

在量子引力的背景场形式主义中，我证明如果量子涨落仅限于微分同胚规范变换而不是物理自由度，就像在传统的量子场论中一样，所有的量子校正都消失在壳上，有效作用是等价的到经典动作。原则上，所得理论是有限且单一的，不需要重整化。我还展示了这是一种独特的参数化，它使路径积分独立于背景字段的壳上条件，一种背景独立性的形式。因此，在背景独立性与可重整性和统一性之间建立了联系。