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。

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.