Research in Gravitational Physics

芝加哥小组关注的是引力物理的广泛研究。与相对论耗散流体理论有关的一些数学问题将被详细研究，特别是耗散流体方程的“N-S极限”，他们将研究具有相同N-S极限的不同流体方程的解如何“接近”彼此的问题。我们将研究建立一个令人满意的、可解释的均匀宇宙量子引力理论的可能性，并研究非均匀宇宙模型的Wheeler-DeWitt方程的性质。他们将研究具有紧凑柯西表面的全球双曲时空中与Hadamard真空态相关的量子场结构的酉等价性问题。此外，还将研究经典广义相对论、弯曲时空中的量子场论和量子引力。所有这些研究的基本目标都是为了更深入地理解经典广义相对论中的数学和物理问题，并在建立引力的量子理论方面取得进展。

The Chicago group is concerned with a broad range of research in gravitational physics. Some mathematical issues related to the theory of relativistic dissipative fluids will be investigated in detail; in particular, the "Navier-Stokes limit" of dissipative fluid equations will be studied and they will investigate the issue of how "close" solutions to different fluid equations having the same Navier-Stokes limit are to each other. The possibility of formulating a satisfactory and interpretable quantum gravity theory for homogeneous cosmologies in analogy with the theory of a relativistic particle will be studied, and properties of the Wheeler-DeWitt equation for inhomogeneous cosmological models will be investigated. They will examine the issue of unitary equivalence of quantum field constructions associated with Hadamard vacuum states in globally hyperbolic spacetimes with a compact Cauchy surface. Numerous additional topics in classical general relativity, quantum field theory in curved spacetime, and quantum gravity will be investigated. The basic goal of all of this research is to obtain a deeper understanding of mathematical and physical issues in classical general relativity, and to make progress toward formulating a quantum theory of gravitation.