A Non-perturbative study of the Riemann-Foss-Witten equations in the presence of a scalar field

We present a study of the Riemann-Foss-Witten equations in the presence of a scalar field. We consider the Lorenz model in which $U(R)$ gauge fields are taken into account. We find that the relation between the scalar and the non-perturbative quantities is the same as for the Lorenz model. We also study the Riemann-Foss-Witten equations in the presence of a scalar field in the first order of the scalar fields. The equations are derived, and used to compute the non-perturbative function of the Riemann-Foss-Witten equations.