Topics in Classical and Quantum Relativity

这个项目研究了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：相对论场论中对称约简的一般理论的构造。量子场沿固定时空任意叶状的幺正动力学演化状态的研究。完成了适用于相对论场论的局部上同调的一般理论（p型守恒定律），包括计算工具的开发和爱因斯坦方程的详细应用。研究广义相对论哈密顿公式中曲率标量作为代表“多指时间”的特权规范变量的地位。引力场理论中渐近对话律新方法的进一步发展与应用。真空度量射流空间参数化的进一步发展与应用。利用参数场论技术对允许两个可交换杀伤向量场的时空Dirac约束量子化进行了严格处理。基于Ashtekar变量和规范量子化结果的量子引力路径积分理论的发展。这些课题的工作目标是提高关于广义相对论、万有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.***