On the CJT formalism in multi-field theories

The issues that arise when using the Comwall-Jackiw-Tomboulis formalism in multi-field theories are investigated. Particular attention is devoted to the interplay between temperature effects, ultraviolet structure, and the interdependence of the gap equations. Results are presented explicitly in the case of the evaluation of the finite temperature effective potential of a theory with two scalar fields which has attracted interest as a toy model for symmetry nonrestoration at high temperatures. The lowest nontrivial order of approximation of the Comwall-Jackiw-Tomboulis effective potential is shown to lead to consistent results, which are relevant for recent studies of symmetry nonrestoration by Bimonte and Lozano.