Topics in Classical and Quantum Relativity

这个项目研究经典相对论和量子相对论中的一些问题，特别是爱因斯坦的引力理论。讨论了以下主题：相对论场论中对称性约化的一般理论的构建。研究沿固定时空的任意层的量子场的么正动力学演化状态。完成了为相对论场论量身定做的局部上同调的一般理论(p形式守恒定律)，包括计算工具的发展和对爱因斯坦方程的详细应用。在广义相对论的哈密顿公式中，曲率标量作为特权正则变量代表“多指时间”的地位的研究。引力场理论中渐近守恒定律的新方法的进一步发展和应用。真空度规喷射空间参数化的进一步开发和应用。用参数化场论的方法严格处理了狄拉克约束量子化允许两个交换杀伤矢量场的时空。基于使用阿什特卡变量和正则量子化得到的结果，发展量子引力中的路径积分理论。这些主题的工作目标是改善关于广义相对论、引力和量子力学的知识状态，以及这些物理学分支之间的相互作用。

***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.***