Arthur Jaffe

Multiple Meron Solutions of the Classical Yang-Mills Equation

Abstract We give a construction for multiple meron-antimeron solutions to the classical SU(2) Yang-Mills field equations. The corresponding charge density is Q(x) = 1 2 ∑ ± γ(x−x i ) , with the xi distinct points on a line. The problem is reduced to the solution of a scalar φ4 equation. We obtain a model with merons connected in pairs.

Rigorous quantum field theory models

Quantum field theory provides a natural framework to describe the interactions between elementary particles. Aside from a program of field theory computations, there has been an interest in qualitative or structural aspects of quantum field theory. We announce here some new progress in this direction. We study two standard nonlinear interactions in two space time dimensions. Our main results include the mathematically rigorous construction of quantum field theory models for these interactions. We consider the interactions \pyp (e.g. the coupling between mesons and neutrons or protons). In the nonrelativistic limit the \(AI/ interaction gives rise to a Yukawa potential between fermions; thus it is called the Yukawa interaction. The field equation for the <£ theory is