Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

We probe the $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ Gross-Neveu model with a source term $J\overline{\Psi }\Psi .$ We find an expression for the renormalization scheme and scale invariant source $Ĵ,$ as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We get a nonperturbative mass gap as the solution of $Ĵ=0.\mathrm{}$ In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for $N>\mathrm{}2.\mathrm{}$