On the Effective Potential for Local Composite Operators

We show that the effective potential for local composite operators is a useful object in studing dynamical symmetry breaking by calculating the effective potential for the local composite operators $\bar{\psi} \psi$ and $\phi^2$ 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 in the CJT effective potential. We compare the results obtained with the results give by the auxiliary field method.