4D Spinfoam模型的全纯简单性约束
Holomorphic Simplicity Constraints for 4d Spinfoam Models
摘要：
在spinfoam模型的框架内，我们重新审视了简化的限制，减少拓扑BF理论的四维黎曼引力。我们使用了SU（2）缠结和自旋网络的旋量形式，它来自于最近发展的SU（2）缠结的U（N）框架和自旋网络和自旋泡沫边界态的扭曲几何方法。使用这些工具，我们能够执行一个全纯/反全纯分裂的简单性约束，并定义一组新的全纯简单性约束，这是等价于标准的经典水平，并可以施加强烈的纠缠在量子水平。然后，我们将展示如何解决这些新的全纯简单性约束使用相干缠绕状态。我们进一步定义了相应的相干自旋网络泛函，并引入了一个新的自旋泡沫模型的基础上，这些全纯简单的约束和振幅的新的相干自旋网络的评估定义的四维黎曼引力。
英文摘要：
Within the framework of spinfoam models, we revisit the simplicity constraints reducing topological BF theory to 4d Riemannian gravity. We use the reformulation of SU(2) intertwiners and spin networks in term of spinors, which has come out from both the recently developed U(N) framework for SU(2) intertwiners and the twisted geometry approach to spin networks and spinfoam boundary states. Using these tools, we are able to perform a holomorphic/anti-holomorphic splitting of the simplicity constraints and define a new set of holomorphic simplicity constraints, which are equivalent to the standard ones at the classical level and which can be imposed strongly on intertwiners at the quantum level. We then show how to solve these new holomorphic simplicity constraints using coherent intertwiner states. We further define the corresponding coherent spin network functionals and introduce a new spinfoam model for 4d Riemannian gravity based on these holomorphic simplicity constraints and whose amplitudes are defined from the evaluation of the new coherent spin networks.
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