On the Effective Potential for Local Composite Operators

We show that the effective potential for local composite operators is a useful object in studying dynamical symmetry breaking by calculating the effective potential for the local composite operators ψψ and φ² in the Gross-Neveu (GN) and O(N) models, respectively. Since the effective potential for local composite operators can be calculated by using the Cornwall-Jackiw-Tomboulis (CJT) effective potential in theory with additional bare mass terms, we show that divergences in the effective potential for local composite operators are the same as those in the CJT effective potential. We compare the results obtained with the results given by the auxiliary field method.