Professor Bernard's research focuses primarily on the nonperturbative effects of the strong interactions. Much of this work is numerical, using the techniques of lattice gauge theory.
In recent years, he has collaborated in these numerical computations with the members of the MILC collaboration, which includes professors and senior researchers at several other US universities. A particular interest is computing the effects of strong interactions on weak interaction processes involving quarks. Such computations are crucial to the interpretation of weak interaction experiments and may ultimately point to new physics beyond the Standard Model of particle physics. Other research interests include the study of chiral lagrangians (which extract physical information about the strong interactions from symmetry principles) and the perturbative calculations needed to relate lattice results to continuum answers.