论文标题
最低阶的可预测Horava重力的规范环量化
Canonical loop quantization of the lowest-order projectable Horava gravity
论文作者
论文摘要
研究了最低点的Horava Gravity的Hamiltonian配方，即所谓的$λ$ - $ r $重力。由于在可投射的Horava重力中选择了首选的叶面，因此该理论中没有局部的哈密顿约束。与一般相对论相反，$λ$ - $ r $重力的约束代数形成了lie代数。通过规范转换，我们进一步获得了$λ$ -R重力理论的连接 - 动力形式主义，其实际$ su（2）$ - 作为配置变量。这种形式主义使我们能够将非扰动环量子重力的方案扩展到$λ$ - $ r $ $重力。虽然量子运动框架与一般相对性相同，但在diffeemorphism-ryphistrism-crististrismaniant Hilbert Space中，可以很好地定义Loop Quantum $λ$ - $ r $ gravity的哈密顿约束操作员。此外，通过引入代表动态时间的全球尘埃自由度，可以定义一个实物的哈密顿操作员在灰尘方面，并获得满足所有约束的物理状态。
The Hamiltonian formulation of the lowest-order projectable Horava gravity, namely the so-called $λ$-$R$ gravity, is studied. Since a preferred foliation has been chosen in projectable Horava gravity, there is no local Hamiltonian constraint in the theory. In contrast to general relativity, the constraint algebra of $λ$-$R$ gravity forms a Lie algebra. By canonical transformations, we further obtain the connection-dynamical formalism of the $λ$-R gravity theories with real $su(2)$-connections as configuration variables. This formalism enables us to extend the scheme of non-perturbative loop quantum gravity to the $λ$-$R$ gravity. While the quantum kinematical framework is the same as that for general relativity, the Hamiltonian constraint operator of loop quantum $λ$-$R$ gravity can be well defined in the diffeomorphism-invariant Hilbert space. Moreover, by introducing a global dust degree of freedom to represent a dynamical time, a physical Hamiltonian operator with respect to the dust can be defined and the physical states satisfying all the constraints are obtained.
