论文标题
在本地正规化路径积分中的量子重力的配置空间
Configuration space for quantum gravity in a locally regularized path integral
论文作者
论文摘要
我们讨论背景字段形式主义中量子重力中度量配置空间的某些方面。我们为欧几里得公制波动的参数化提供了必要的条件，以便i）i）在进入引力路径积分的所有配置中，保留了度量的特征，并且ii）参数化提供了在固定背景的完整欧几里得指标和公制波动之间提供的两种射击图。对于叶状歧管的情况，我们将展示如何参数化波动以保留所有配置的略带性。此外，我们明确地表明，通过不平等约束，最方便地实现了Lorentzian量子重力路径积分的配置空间上的签名。我们讨论了在非扰动重新归一化组设置中这些不平等约束的实现。
We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parameterization of Euclidean metric fluctuations such that i) the signature of the metric is preserved in all configurations that enter the gravitational path integral, and ii) the parameterization provides a bijective map between full Euclidean metrics and metric fluctuations about a fixed background. For the case of foliatable manifolds, we show how to parameterize fluctuations in order to preserve foliatability of all configurations. Moreover, we show explicitly that preserving the signature on the configuration space for the Lorentzian quantum gravitational path integral is most conveniently achieved by inequality constraints. We discuss the implementation of these inequality constraints in a non-perturbative renormalization group setup.
