论文标题
欧几里得LQG的无异常量子动力学
Anomaly free quantum dynamics for Euclidean LQG
论文作者
论文摘要
经典引力进化在尺寸衍生物的量规协变概括方面接受了优雅而紧凑的重新表达。欧几里得环量子重力的量子动力学归因于电动移位算子的中心作用[2]。 $ there \;我们\;展示\;那\;这个\;量子\;动力学\;是\;非定性\;异常$ $ $ $。具体而言，我们表明，在一对哈密顿约束操作员之间的（非悬而未决的）换向器上（a）在经典通讯员之间的泊松支架，（b）有限的空间差异群体忠实地代表了哈米尔顿（Hamilton）的行动，（c）co的行动是（C）差异性。
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric Shift [1]. A quantum dynamics for Euclidean Loop Quantum Gravity which ascribes a central role to the Electric Shift operator is derived in [2]. $Here\; we\; show\; that\; this \;quantum\; dynamics\; is\; nontrivially\; anomaly$ $free$. Specifically, we show that on a suitable space of off shell states (a) the (non-vanishing) commutator between a pair of Hamiltonian constraint operators mirrors the Poisson bracket between their classical correspondents, (b) the group of finite spatial diffeomorphisms is faithfully represented and (c) the action of the Hamiltonian constraint operator is diffeomorphism covariant with respect to the action of spatial diffeomorphisms.
