论文标题
LQG中宇宙相干状态期望值的算法方法
Algorithmic approach to Cosmological Coherent State Expectation Values in LQG
论文作者
论文摘要
在固定图计算上循环量子重力的晶格方法中，往往涉及，并且很少在分析上可管理。但是，当对晶格上相干状态的期望值感兴趣时，在各向同性宇宙学上峰值达到峰值，可以简化一些简化，从而减少计算工作。我们提出了一种逐步算法，导致分析表达式，包括状态扩散中的一阶校正。该算法的开发方式使其可以直接且易于在编程语言（例如Mathematica）中实现。示例性地，我们证明了该算法如何简化标量约束的欧几里得部分的期望值并作为一致性检查也执行分析计算。为了展示该算法的进一步应用，我们研究了有效的动力学计划在循环宇宙学中的命运，并发现近临界的顺序更正可以用作有效的汉密尔顿人的校正。
In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply peaked on isotropic, flat cosmology several simplifications are possible which reduce the computational effort. We present a step-by-step algorithm resulting in an analytical expression including up to first order corrections in the spread of the state. The algorithm is developed in such a way that it makes the computation straightforward and easy to be implementable in programming languages such as Mathematica. Exemplarily, we demonstrate how the algorithm streamlines the road to obtain the expectation value of the euclidean part of the scalar constraint and as a consistency check perform the analytic computation as well. To showcase further applications of the algorithm, we investigate the fate of the effective dynamics program custom in Loop Cosmology and find that the next-to-leading order corrections can {\it not} be used as corrections for an effective Hamiltonian.
