常曲率弯曲时空中的量子化及效应的研究

Quantum field theory in curved spacetime is an important footprint towards the theory of everything. After the discovery of cosmic acceleration, de Sitter relativity with positive constant curvature attracted wide interest. de Sitter special relativity with Beltrami metric and Beltrami coordinates(BdS) is an important domestic original work. As a combination of these three areas, quantizing theories in the classical BdS spacetime would be promising...This project plans to study the quantization and effects in BdS curved spacetime with constant curvature..<1> Construct quantum field theory in BdS curved spacetime..<2> The corresponding quantum effect of inertial forces is Unruh effect: when a quantum field in inertial BdS frames is in vacuum state, an inertial observer in BdS spacetime does not see particles, but a particle detector carried by an accelerating observer would see a thermal spectrum of particles at Unruh temperature. The effect will be calculated through Bogolyubov transformation between two vacua. Schwarzschild-BdS, Kerr-Newman-BdS and other new metrics would be used to research Hawking radiation. With vacuum state defined in asymptotically BdS spacetime region, the temperature and entropy of Hawking radiation will be calculated..<3> Actively seek to be combined with the frontier of astronomical discoveries..Progress in this project would help promote the development of gravitation and cosmology and reveal some features of quantum gravity.

弯曲时空量子场论，是通往万有理论的重要脚印。因为宇宙是加速膨胀的，正的常曲率弯曲时空，是广义相对论研究的重要对象。采用Beltrami坐标(BdS)的de Sitter狭义相对论，是国人获得的重要原始创新工作。把三者结合，在经典的BdS时空背景中做量子化，大有可为。本项目拟研究BdS常曲率弯曲时空中的量子化及效应。<1>构建BdS常曲率弯曲时空中的量子场论。<2>研究惯性力对应的量子效应，计算Bogolyubov变换，讨论惯性坐标系的BdS真空由非惯性系观测者看应测到的Unruh温度。基于预研新得的Schwarzschild-BdS和Kerr-Newman-BdS等时空，在无穷远处渐近BdS的时空中定义真空态，研究霍金辐射。<3>主动寻求和天文观测前沿结合。深入研究有助于推动引力和宇宙学相关领域的发展，有助于摸索量子引力的某些特征。

采用Beltrami坐标(BdS)，研究了德西特常曲率弯曲时空背景下的量子化和效应。考虑BdS时空或无穷远处渐近BdS的时空，对于普通德西特参考系和BdS参考系的观测者，分别定义真空态。论证发现普通德西特参考系的观测者的真空态，由BdS参考系的观测者来测，能测到粒子。此处Unruh效应获得证实，展示了BdS研究的科学意义。考虑史瓦兹-BdS黑洞，求得其黑洞视界和宇宙视界。计算霍金辐射，得到对温度的更全面修正，其中一项修正，和且只和选用BdS参考系相关。考虑史瓦兹-BdS弯曲时空中光线偏折问题，计算得到对偏折角的更全面修正。修正精确到GM的二阶和宇宙学常数Λ的二阶，比现有文献阶数高，还发现依赖且只依赖于BdS坐标的新修正项。结合观测数据，R的下限取得新估值。本项目在BdS常曲率弯曲时空的量子效应和引力效应做出新进展，有助于摸索量子引力的某些特征。