### Speaker

### Description

Establishing a description for confinement is not something simple. In order to try to understand a little about this phenomenon, we will explore the thermodynamics of models that try to describe it in terms of propagators with violation of positivity. In this work, "confinement'' is always understood in the sense of positivity violation of the propagator of the elementary fields. For simplicity, we will define a model for scalar fields with a momentum dependent and nonlocal mass term. The (euclidian) Lagrangian for such a toy model is given by

\begin{equation}

{\cal L}_E = \frac{1}{2} \left[ \phi(x) \left( -\partial^2 + m^2 +\frac{\Lambda^4}{-\partial^2 + M^2} \right) \phi(x) \right] \; .

\end{equation}

A Lagrangian written in this way is analogous to the refined Gribov-Zwanziger (RGZ) Lagrangian and has a similar propagator to the gluon propagator in the lattice. One of our objectives is to verify the thermodynamic properties of this Lagrangian in order to analyze possible inconsistencies. For this we use the functional formalism of Quantum Field Theory at finite temperature, from which we obtain the partition function and, consequently, the thermodynamic variables such as pressure, energy density, entropy density, etc. Then, we obtain the two-point function at finite temperature of the scalar field $\phi$, in order to study whether or not there is a restoration of positivity (hence, deconfinement, in our language). Finally, we obtain the first order perturbative correction for the partition function and for thermodynamic variables considering an auto-interaction potential of type $\phi^4$.