论文标题
自旋泡沫作为半古典顶点：胶合限制和混合算法
Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
论文作者
论文摘要
在过去的几年中，自旋FOAM模型中的数值方法已显着提高，但是在有效提取具有许多量子自由度的幅度的结果中，挑战仍然存在。在本文中，我们绘制了``混合算法''的建议，该提案将同时在相关策略中同时使用完整的量子幅度及其渐近近似。作为迈向算法的第一步，我们得出了分区函数的新表示形式，其中每个旋转泡沫顶点都具有自己的相干数据，因此可以单独渐近地近似。我们通过在顶点之间实现胶合约束来做到这一点，我们在数值上研究。我们进一步得出了任意边界数据约束的渐近表达式，包括没有关键点的数据。从这个新表示形式中，我们猜想了一种中间的准几何旋转泡沫制度，描述了通过胶合约束以非匹配方式粘合的半古典顶点的叠加。
Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a ``hybrid algorithm'' that would use both the full quantum amplitude and its asymptotic approximation in the relevant regimes. As a first step towards the algorithm, we derive a new representation of the partition function where each spin-foam vertex possesses its own coherent data, such that it can be individually asymptotically approximated. We do this through the implementation of gluing constraints between vertices, which we study numerically. We further derive an asymptotic expression for the constraints for arbitrary boundary data, including data for which there are no critical points. From this new representation we conjecture an intermediate quasi-geometric spin-foam regime describing a superposition of semi-classical vertices glued in a non-matching way via the gluing constraints.
