论文标题
量子重力，恒定负曲率和黑洞
Quantum Gravity, Constant Negative Curvatures, and Black Holes
论文作者
论文摘要
出于量化的目的，经典的重力通常由规范变量表示，即公制$ g_ {ab}（x）$和动量$π^{cd}（x）$。规范量化要求将这些经典变量正确促进到量子运算符，根据迪拉克（Dirac）的说法，最喜欢的操作员应该是由形成笛卡尔坐标的经典变量引起的。可悲的是，在这种情况下，这是不可能的。但是，促进度量$ g_ {ab}（x）$的仿射量化功能和矩$π^c_d（x）\; [\equivπ^{ce}（x）\，g_ {de}（x）（x）（x）] $。它们属于恒定的曲率空间（即，而不是平坦的空间），而不是这些经典变量，而是属于恒定负曲线的空间。此功能甚至可能在黑洞中出现，这可能强烈指向量化重力的仿射量化方法。
For purposes of quantization, classical gravity is normally expressed by canonical variables, namely the metric $g_{ab}(x)$ and the momentum $π^{cd}(x)$. Canonical quantization requires a proper promotion of these classical variables to quantum operators, which, according to Dirac, the favored operators should be those arising from classical variables that formed Cartesian coordinates; sadly, in this case, that is not possible. However, an affine quantization features promoting the metric $g_{ab}(x)$ and the momentric $π^c_d(x)\;[\equiv π^{ce}(x) \,g_{de}(x)]$ to operators. Instead of these classical variables belonging to a constant zero curvature space (i.e., instead of a flat space), they belong to a space of constant negative curvatures. This feature may even have its appearance in black holes, which could strongly point toward an affine quantization approach to quantize gravity.
