标题： 量子引力中可量化几何的必要性 显示英文标题

标题： Necessity of Quantizable Geometry for Quantum Gravity

摘要： 在本文中，尝试在第一性形式中对$3D$引力进行狄拉克量子化，其中不是对连接和三重场进行量子化，而是对连接和三重1-形式本身进行量子化。 微分形式空间上的外导数算子被当作“时间”导数，以计算这些1-形式的共轭动量。 这种量子化方法使得能够计算$3D$引力中的跃迁振幅，该振幅与通过LQG技术计算得到的跃迁振幅有密切但不完全吻合的匹配。 这种不一致被解释为微分几何不可量子化的性质所致。 显示英文摘要

摘要： In this paper, Dirac Quantization of $3D$ gravity in the first-order formalism is attempted where instead of quantizing the connection and triad fields, the connection and the triad 1-forms themselves are quantized. The exterior derivative operator on the space of differential forms is treated as the `time' derivative to compute the momenta conjugate to these 1-forms. This manner of quantization allows one to compute the transition amplitude in $3D$ gravity which has a close, but not exact, match with the transition amplitude computed via LQG techniques. This inconsistency is interpreted as being due to the non-quantizable nature of differential geometry.