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

Abstract

We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi }\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, 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 non-perturbative mass gap as the solution of $\hat{J}=0$. 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>2.

13 pages, 3 figures, added reference

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