In this talk, we address a foundational challenge in quantum field theory on curved spacetime by constructing a consistent framework within loop quantum gravity. We introduce a methodology to define meaningful superpositions of quantum geometry and matter states. This is achieved by identifying a restricted subspace of the gravitational phase space, ensuring unitary equivalence among Fock representations for a scalar field across different quantum geometries. Within the resulting well-defined Hilbert space, we derive weak solutions to the quantum Hamiltonian constraint of general relativity. These solutions inherently encode entanglement between geometry and matter. Furthermore, we generalize the Hartle-Hawking vacuum state to this quantum geometric context. The resulting vacuum is intrinsically entangled with the quantum geometry. 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.

Biography

龙高平副教授，目前就职于暨南大学物理与光电工程学院；于2020年6月毕业于北京师范大学并获得博士学位，2020年7月至2023年4月在华南理工大学进行博士后研究工作；主要研究方向为圈量子引力及高维引力理论，目前已在 Phys. Rev. D、Eur. Phys. J. C、Phys. Lett. B 等学术期刊发表十余篇学术论文，并主持国家自然科学基金青年基金（C类）和专项项目各一项。

Inviter: Jie-Qiang Wu