论文标题
量子重力和模糊球上的riemannian几何形状
Quantum Gravity and Riemannian Geometry on the Fuzzy Sphere
论文作者
论文摘要
我们研究了模糊球的量子几何形状定义为角动量代数$ [x_i，x_j] = 2 \imathλ_pε_{ijk} x_k $ modulo设置$ \ sum_i x_i x_i x_i x_i^2 $，使用最近引入的3D旋转旋转式不同的旋转式不同的旋转式不同。指标由对称$ 3 \ times 3 $矩阵$ g $给出，我们证明，对于每个指标，都有一个独特的量子levi-civita连接，具有恒定系数，带有标态曲率$ \ frac {1} {1} {2} {2} {2}（{\ rm tr}（\ rm tr}（g^2） - \ frac - \ frac {1} {1} {1} {2} {2} {2} {2} tr}（g）^2）/\ det（g）$。作为一种应用，我们在模糊单元球上构建欧几里得量子重力。我们还计算3D差分结构的电荷1单极。
We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imathλ_p ε_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant differential structure. Metrics are given by symmetric $3 \times 3$ matrices $g$ and we show that for each metric there is a unique quantum Levi-Civita connection with constant coefficients, with scalar curvature $ \frac{1}{2}({\rm Tr}(g^2)-\frac{1}{2}{\rm Tr}(g)^2)/\det(g)$. As an application, we construct Euclidean quantum gravity on the fuzzy unit sphere. We also calculate the charge 1 monopole for the 3D differential structure.
