Topics in Classical and Quantum Relativity

* 9732636 Torre这个项目研究了经典和量子相对论中的一些问题，特别是爱因斯坦的引力理论。 以下主题是解决：建设的一般理论对称性减少相对论性场论。量子场沿固定时空沿着任意叶理的幺正动力学演化状态的研究。完成针对相对论场论的局部上同调（p-形式守恒定律）的一般理论，包括开发计算工具和爱因斯坦方程的详细应用。曲率标量作为代表“多指时间”的特权正则变量在广义相对论哈密顿公式中的地位的研究。引力场理论中渐近守恒律新方法的进一步发展和应用。真空度规喷流空间参数化的进一步发展和应用。严格处理狄拉克约束量子化的时空，允许两个交换的基灵向量场使用参数化场论的技术。基于使用Ashtekar变量和正则量子化获得的结果，发展量子引力中的路径积分理论。这些主题的工作目标是提高关于广义相对论，引力和量子力学以及这些物理分支之间相互作用的知识水平。

***9732636TorreThis project investigates a number of issues and problems in classical and quantum relativity and, in particular, Einstein's theory of gravitation. The following topics are addressed: Construction of a general theory of symmetry reduction in relativistic field theories. Investigation of the status of unitary dynamical evolution of quantum fields along arbitrary foliations of a fixed spacetime. Completion of a general theory of local cohomology (p-form conservation laws) which is tailored to relativistic field theory, including development of computational tools and detailed applications to the Einstein equations. Investigation of the status of curvature scalars as privileged canonical variables representing "many-fingered time" in the Hamiltonian formulation of general relativity. Further development and applications of a new approach to asymptotic conversation laws in gravitational field theory. Further development and applications of a parametrization of the jet space of vacuum metrics. Rigorous treatment of Dirac constraint quantization of spacetimes admitting two commuting Killing vector fields using the techniques of parametrized field theory. Development of a theory of path integrals in quantum gravity based upon results obtained using Ashtekar variables and canonical quantization.The goal of work on these topics is to improve the state of knowledge regarding general relativity, gravitation, and quantum mechanics as well as the interaction of these branches of physics.***