My work addresses fundamental questions in quantum physics, including the quantization of vortex motion in ideal superfluids, the quantum field theory of anyons in 2+1 dimensions, generalized configuration spaces for statistical and quantum physics, non-Abelian Born-Infeld and other generalizations of the Yang-Mills equations, and various nonlinear modifications of quantum mechanics. My interests also include representations of infinite-dimensional Lie algebras (current algebras) and groups as applied in quantum theory.
My research is focused primarily on the foundations of quantum mechanics, and in particular on the heretical version of nonrelativistic quantum mechanics known as Bohmian mechanics. The work involves both the mathematical, physical, and conceptual analysis of Bohmian mechanics itself as well as the search for suitable relativistic extensions. The goal is to understand exactly what quantum theory says and why nature should be governed by anything so bizarre as quantum theory.
My work covers a wide variety of problems in equilibrium and non-equilibrium statistical mechanics and involves a mixture of rigorous and non-rigorous methods. The main theme of the work is the microscopic origin of macroscopic behavior. This includes: 1) Phase transitions in equilibrium and non-equilibrium systems; 2) Derivation of hydrodynamical equations from microscopic kinetics; 3) Phase segregation dynamics; 4) Statistical mechanics of plasmas; 5) Time evolution of micro- and macro-quantum systems.
Revised September, 2019