Numerical Studies in Quantum Field Theory and Critical Phenomena

理论物理的研究将处于基本粒子物理和统计物理之间的交界处，将这两个领域的方法应用到各自的问题上。基本粒子物理学的研究将集中在量子色动力学的数值研究上，这是日益得到证实的关于强大亚核力的详细理论。为了检验最近提出的夸克禁闭理论，将用数值方法计算一对夸克之间的相互作用能。统计物理学的研究将侧重于通过开发和应用新的和更有效的“蒙特卡罗”计算方法，对被称为“临界现象”的一类相变进行数值阐明。该方法包括启发式物理推理、严格的数学分析和系统的数值测试相结合。特别是，对自回避随机游动的研究将直接应用于聚合物分子在稀溶液中的行为。

Research in theoretical physics will lie at the interface between elementary-particle physics and statistical physics, applying methods from both fields to problems in each. Investigations in elementary-particle physics will focus on numerical study of quantum chromodynamics, which is the increasingly-confirmed detailed theory of the strong subnuclear force. The interaction energy between a pair of quarks will be calculated numerically, with the aim of testing a recently proposed theory of quark confinement. Investigations in statistical physics will focus on numerical elucidation of the class of phase transitions known as "critical phenomena", by developing and applying new and more efficient "Monte Carlo" methods of calculation. The methodology involves a combination of heuristic physical reasoning, rigorous mathematical analysis, and systematic numerical testing. In particular, study of the self-avoiding random walk will have direct applications to the behavior of polymer molecules in dilute solution.