群场论中的关系动力学与Page-Wootters形式
Relational dynamics and Page-Wootters formalism in group field theory
AI总结：
本文利用参数化群场论与Dirac量子化纲领，证明“时钟中性”理论等价于基于Page-Wootters形式的去参数化正则群场论，首次将该形式直接应用于非微扰量子引力，并扩展至多规范对称性设置。
摘要：
群场论（Group field theory）假设时空是演生的，因此其定义不依赖于任何背景空间或时间的概念；动力学问题以关系术语来表述，特别是使用（标量）物质自由度作为时间。与引力系统的正则量子化不同，这里没有明显的坐标变换或约束的概念，且既有的量子化方法无法直接应用。因此，文献中已讨论了群场论的不同正则形式。我们使用参数化版本的群场论来解决这些问题，其中所有（几何和物质）自由度都在一个基准参数中演化。存在一个与重参数化自由度相关的约束，并且可以实现Dirac量子化纲领。利用“关系动力学三位一体”，我们证明由此得到的“时钟中性”理论完全等价于去参数化的正则群场论，后者用Page-Wootters形式来解释。我们的结果不仅表明去参数化量子化是完全协变的，并且可被视为编码了量子物质与几何联合自由度的动力学，它们似乎也是Page-Wootters形式直接应用于非微扰量子引力的首次尝试。我们展示了向引入许多独立规范对称性设置的扩展，这与量子引力中的“多指时间”思想相联系，并为Page-Wootters形式提供了一个略显新颖的扩展。
英文摘要：
Group field theory posits that spacetime is emergent and is hence defined without any background notion of space or time; dynamical questions are formulated in relational terms, in particular using (scalar) matter degrees of freedom as time. Unlike in canonical quantisation of gravitational systems, there is no obvious notion of coordinate transformations or constraints, and established quantisation methods cannot be directly applied. As a result, different canonical formalisms for group field theory have been discussed in the literature. We address these issues using a parametrised version of group field theory, in which all (geometry and matter) degrees of freedom evolve in a fiducial parameter. There is a constraint associated to the freedom of reparametrisation and the Dirac quantisation programme can be implemented. Using the "trinity of relational dynamics", we show that the resulting "clock-neutral" theory is entirely equivalent to a deparametrised canonical group field theory, interpreted in terms of the Page-Wootters formalism. Our results not only show that the deparametrised quantisation is fully covariant and can be seen as encoding the dynamics of joint quantum matter and geometry degrees of freedom, they also appear to be the first application of the Page-Wootters formalism directly to non-perturbative quantum gravity. We show extensions to a setting in which many independent gauge symmetries are introduced, which connects to the "multi-fingered time" idea in quantum gravity and provides a somewhat novel extension of the Page-Wootters formalism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
