Numerical Studies in Quantum Field Theory and Critical Phenomena

理论物理学的研究将处于基本粒子物理学和统计物理学的交界，将这两个领域的方法应用于各自领域的问题。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，量子色动力学是强亚核力的一个日益得到证实的详细理论。一对夸克之间的相互作用能量将被数值计算，目的是测试最近提出的夸克约束理论。统计物理学的研究将集中于通过发展和应用新的更有效的“蒙特卡罗”计算方法，对被称为“临界现象”的相变进行数值解释。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。特别是对聚合物分子在稀溶液中的自回避随机游走行为的研究，将对聚合物分子在稀溶液中的行为具有直接的应用价值。

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.