Yang-Mills instantons and the S-matrix

We present a scheme for calculating gauge-invariant S-matrix elements in the presence of instantons. We exploit the conformal invariance of the zero-mass field equations. The asymptotic in and out states are defined by their values on null infinity $\text{J}$. We use this method to calculate to lowest-order S-matrix elements for scalar particles and fermions in a dilute gas of SU(2) instantons and anti-instantons. The scalar particles acquire an effective mass and an effective interaction of the form $\text{exp}\text{(?(?}{}^2\text{/16π) ?}\text{?}\text{)}$, where ? is the scale of the instanton, plus other interactions which cannot be presented by a local effective lagrangian. The fermions acquire the effective lagrangian obtained by 't Hooft. In the case of a single flavour of fermions, this corresponds to a mass term.