Mathematical Sciences: Constructive Computer Methods Appliedto Problems in Statistical Mechanics and Quantum Field Theory

本研究项目计划结合PI等人开发的一些计算机辅助方法，构建在三维空间中控制临界晶格系统红外行为的重整化群不动点，如临界phi 4/3标量量子场模型或三维Ising模型。它还计划得到这些模型的（通用）临界指数的严格界限。得到这些三维模型的严格结果的工作将在一台超级计算机上完成。量子场论旨在为现实的量子物理模型建立一个严格的数学结构。从该理论中推断出的结论将增强我们对量子物理学的理解，并使我们能够利用这种新的理解来实现新的创新技术进步。

This research project plans to combine a number of computer-assisted methods developed by the PI and others and construct the renormalization group fixed point which governs the infrared behavior of critical lattice systems in three dimensions, such as the critical phi 4/3 scalar quantum field model or the three dimensional Ising model. It also plans to get rigorous bounds on the (universal) critical exponents of these models. The work to get the rigorous results for these three dimensional models will be done on a supercomputer. Quantum field theory is aimed at a rigorous mathematical construct for quantum physical models of reality. Conclusions deduced from the theory will enhance our understanding of quantum physics and allow us to exploit this new understanding for new and innovative technological advances.