arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2602.14282gr-qc
收藏

量子场论中的量子几何效应:哈密顿约束产生引力-物质纠缠

Quantum Geometry Effects in Quantum Field Theory: Hamiltonian constraint Generates Gravity-Matter Entanglement

School of Physics and Astronomy, Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing Normal University(北京师范大学物理与天文学院,教育部多尺度自旋物理重点实验室)

Gaoping Long, Cong Zhang

AI总结:

本文提出了一种在圈量子引力框架下研究几何-物质纠缠的方法,并推导了广义相对论量子哈密顿约束的弱解。

摘要:

本文针对弯曲时空上量子场论中的基础挑战,发展了一个在圈量子引力内的一致框架。我们引入了一种定义有意义的量子几何和物质态叠加的方法。这通过识别引力相空间的一个受限子空间来实现,该子空间确保了标量场的不同量子几何的福克表示之间的一致性。在由此得到的明确状态空间中,我们推导出广义相对论量子哈密顿约束的弱解。此外,我们将哈特尔-霍金真空态推广到这个量子几何框架中。所得到的状态表现出几何与物质之间的内在纠缠,这种纠缠源自广义相对论的量子哈密顿约束。这项工作建立了一个研究几何-物质纠缠的原理性框架,并为黑洞信息悖论的量子基础提供了新的见解。

英文摘要:

In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum geometry and matter states. This is achieved by identifying a restricted subspace of the gravitational phase space, which ensures unitary equivalence among Fock representations of a scalar field across different quantum geometries. Within the resulting well-defined state space, we derive weak solutions to the quantum Hamiltonian constraint of general relativity. Furthermore, we generalize the Hartle-Hawking vacuum state to this quantum geometric framework. The resulting state exhibits the inherent entanglement between geometry and matter, which arises from the quantum Hamiltonian constraint of general relativity. This work establishes a principled framework for studying geometry-matter entanglement and offers new insights into the quantum foundations of the black hole information paradox.

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。

↑