论文标题
新的路径积分公式的半经典限制来自降低相位循环量子重力
Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
论文作者
论文摘要
最近，在ARXIV：1910.03763中得出了一个新的路径积分公式，该公式是根据规范LQG的减少相空间公式的。本文着重于该路径积分公式的半经典分析。我们表明，路径积分的主要贡献来自半经典运动方程（EOMS）的解决方案，该方程还原为汉密尔顿的全能和通量方程$ {h}（e），{p}^a（e）^a（e）$在减少的相位空间$ \ nathcal $ \ nathcal {p}_γ$ $ cubic $ $ $ $ ustice $ $ strace的相位空间中$ \ dot {h}（e）= \ {{{h}（e），\，\，\，\ mathbf {h} \} $，$ \ dot {p}^a（e）= \ {{p} {p}^a（e），\，\，\，\ mathbf {哈密顿。来自路径积分的半经典动力学成为$ \ Mathcal {p}_γ$中哈密顿时间演变的初始值问题。此外，当我们采用晶格$γ$的连续限制时，这些汉密尔顿的方程可正确地繁殖经典的经典减少的重力相位，耦合到连续体的尘埃场，就初始和最终状态而言，这是半经典的。我们的结果证明了新的路径积分公式具有正确的半经典限制，并表明LQG中的相位空间量化减少在半经验上是一致的。基于这些结果，我们比较了此路径积分配方和自旋泡沫配方，并表明该配方具有多个优点，包括有限性，与规范的LQG关系以及没有余弦和平坦性问题。
Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path integral formulation. We show that dominant contributions of the path integral come from solutions of semiclassical equations of motion (EOMs), which reduces to Hamilton's equations of holonomies and fluxes ${h}(e),{p}^a(e)$ in the reduced phase space $\mathcal{P}_γ$ of the cubic lattice $γ$: $\dot{h}(e)=\{{h}(e),\, \mathbf{H}\}$, $\dot{p}^a(e)=\{{p}^a(e),\, \mathbf{H}\}$, where $\mathbf{H}$ is the discrete physical Hamiltonian. The semiclassical dynamics from the path integral becomes an initial value problem of Hamiltonian time evolution in $\mathcal{P}_γ$. Moreover when we take the continuum limit of the lattice $γ$, these Hamilton's equations reproduce correctly classical reduced phase space EOMs of gravity coupled to dust fields in the continuum, as far as initial and final states are semiclassical. Our result proves that the new path integral formulation has the correct semiclassical limit, and indicates that the reduced phase space quantization in LQG is semiclassically consistent. Based on these results, we compare this path integral formulation and the spin foam formulation, and show that this formulation has several advantages including the finiteness, the relation with canonical LQG, and being free of cosine and flatness problems.
