CORNWALL–JACKIW–TOMBOULIS EFFECTIVE POTENTIAL FOR CANONICAL NONCOMMUTATIVE FIELD THEORIES

We apply the Cornwall–Jackiw–Tomboulis (CJT) formalism to the scalar λφ4 theory in canonical-noncommutative space–time. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter θμν. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case (θμν=0), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies, suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.

THE COMPOSITE OPERATOR (CJT) FORMALISM IN THE (λφ4 + ηφ6)D=3 MODEL AT FINITE TEMPERATURE

We discuss the three-dimensional λφ4+ηφ6 theory in the context of the 1/N expansion at finite temperature. We use the method of the composite operator (CJT) for summing a large set of Feynman graphs. We analyze the behavior of the thermal square mass and the thermal coupling constant in the low and high temperature limits. The existence of the tricritical point at some temperature is found using this method.