Ashtekar和Lagrange-Finsler变量中的圈量子引力与广义相对论的Fedosov量子化
Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity
摘要：
我们提出了一个统一的方法，以环量子引力和引力的Fedosov量子化的几何形状的双时空纤维化及其量子形变。考虑伪Riemannian流形，其具有1）定义非线性连接（N-连接）结构的非完整2+2分布和2）Arnowitt-Deser-Misner 3+1分解。Ashtekar-Barbero变量被推广到N-连接结构中，这使得我们可以用Lagrange-Finsler变量和相关的正则几乎辛形式和连接等价地写出广义相对论。重新定义了类引力规范连接的Fedosov结果，分析了在圈量子引力中用几何对象计算形变量子化的星积的条件.我们推测量子引力理论与3+1和2+2分裂的等价性以及爱因斯坦方程的量子类似物。
英文摘要：
We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo-Riemannian manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear connection (N-connection) structure and 2) an Arnowitt-Deser-Misner 3+1 decomposition. The Ashtekar-Barbero variables are generalized and adapted to the N-connection structure which allows us to write the general relativity theory equivalently in terms of Lagrange-Finsler variables and related canonical almost symplectic forms and connections. The Fedosov results are re-defined for gravitational gauge like connections and there are analyzed the conditions when the star product for deformation quantization is computed in terms of geometric objects in loop quantum gravity. We speculate on equivalence of quantum gravity theories with 3+1 and 2+2 splitting and quantum analogs of the Einstein equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
