标题： 广义相对论和爱因斯坦-布里渊-凯勒量子化的辛结构 显示英文标题

标题： Symplectic structure for general relativity and Einstein-Brillouin-Keller quantization

摘要： 基于辛几何理论，讨论了广义相对论的哈密顿系统及其在无任何物质或规范场情况下的量子化。 利用纯引力的广义相空间构造经典广义相对论的辛几何。 按照几何量子化的标准程序对辛流形进行预量子化。 在爱因斯坦-布里渊-凯勒量子化条件之下，从经典解中选取量子真空解。 通过预量子化丛实现量子解的拓扑修正，即Maslov指标。 此外，还讨论了Schwarzschild黑洞可能的质量谱。 显示英文摘要

摘要： The Hamiltonian system of general relativity and its quantization without any matter or gauge fields are discussed on the basis of the symplectic geometrical theory. A symplectic geometry of classical general relativity is constructed using a generalized phase space for pure gravity. Prequantization of the symplectic manifold is performed according to the standard procedure of geometrical quantization. Quantum vacuum solutions are chosen from among the classical solutions under the Einstein-Brillouin-Keller quantization condition. A topological correction of quantum solutions, namely the Maslov index, is realized using a prequantization bundle. In addition, a possible mass spectrum of Schwarzschild black holes is discussed.