通过Pachner移动的洛伦兹量子引力：单圈计算
Lorentzian quantum gravity via Pachner moves: one-loop evaluation
AI总结：
本研究验证了洛伦兹Regge路径积分可解决欧几里得量子引力的共形因子问题，通过Pachner移动分离引力作用量的不定号特性，构建3维离散化不变的局部路径积分测度，为非微扰洛伦兹路径积分的存在性研究奠定基础。
摘要：
洛伦兹量子引力被认为能够解决欧几里得量子引力中遇到的问题，比如共形因子问题。我们证明了在平直背景附近展开的洛伦兹Regge路径积分确实如此。我们阐释了三角剖分的一类局部变化（即Pachner移动）如何在离散层面上分离出引力作用量的不定号特性，这一特性可通过选取相反的变形积分围道来解释。此外，我们为3维洛伦兹Regge微积分构建了一种离散化不变的局部路径积分测度，并指出在4维中定义此类测度存在的障碍。我们将本工作视为确立Regge微积分及自旋泡沫等相关框架的非微扰洛伦兹路径积分存在性的第一步。详尽的附录概述了洛伦兹Regge微积分，使用了最近引入的复化Regge作用量概念，并推导了正文所需的实用几何公式与恒等式。
英文摘要：
Lorentzian quantum gravity is believed to cure the pathologies encountered in Euclidean quantum gravity, such as the conformal factor problem. We show that this is the case for the Lorentzian Regge path integral expanded around a flat background. We illustrate how a subset of local changes of the triangulation, so-called Pachner moves, allow to isolate the indefinite nature of the gravitational action at the discrete level. The latter can be accounted for by oppositely chosen deformed contours of integration. Moreover, we construct a discretization-invariant local path integral measure for 3D Lorentzian Regge calculus and point out obstructions in defining such a measure in 4D. We see the work presented here as a first step towards establishing the existence of the non-perturbative Lorentzian path integral for Regge calculus and related frameworks such as spin foams. An extensive appendix provides an overview of Lorentzian Regge calculus, using the recently introduced concept of the complexified Regge action, and derives useful geometric formulae and identities needed in the main text.
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。
