引力量子理论
A quantum theory of gravity
- Higher Polytechnic School, Autonomous University of Madrid（马德里自治大学高等理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于本征时间演化的协变哈密顿量子引力理论，通过观测者汇投影和正则量子化，解决了宇宙学、黑洞及黑洞热力学中的奇点问题。
AI中文摘要：
我们发展了一种协变哈密顿形式体系，其中演化沿观测者汇的本征时间流进行测量，用李导数取代外部坐标时间导数。我们的形式体系保留了演化变量与构型变量之间的哈密顿量分解，并通过相对于所选观测者汇投影的时空张量来表达。量子化后，所得的观测者汇对易括号导致相对论性的海森堡方程和薛定谔方程，其演化参数为本征时间。然后，我们将该框架应用于引力，取投影空间度规及其共轭动量为正则变量，从而获得正则量子引力的完整模型。在该理论的预言中，我们找到了对宇宙学、黑洞和黑洞热力学中奇点问题的解决。
英文摘要：
We develop a covariant Hamiltonian formalism in which evolution is measured along the proper-time flow of an observer congruence, replacing the external coordinate-time derivative with the Lie derivative. Our formalism keeps the Hamiltonian split between evolution and configuration variables and expresses it through spacetime tensors projected relative to the chosen congruence. After quantization, the resulting observer-congruent brackets lead to relativistic Heisenberg and Schrödinger equations whose evolution parameter is proper time. We then apply this framework to gravity by taking the projected spatial metric and its conjugate momentum as canonical variables, obtaining a complete model of canonical quantum gravity. Among the predictions of this theory we find a resolution to the singularity problems in cosmology, black holes and black hole thermodynamics.
