Numerical Studies in Quantum Field Theory and Critical Phenomena

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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.