Resummation in Hot Field Theories

We consider a scalar theory at finite temperature in the 2PI resummation scheme, including ϕ³ and ϕ⁴ interactions. Already at the one loop level in this scheme, we have to deal with a non local approximation. We carry out the renormalization and obtain finite equations for the propagator. Within this model we can explore the effect of non local contributions to the self-energy in the evaluation of thermodynamic quantities.