Exploring the Thermodynamics of Confining Models

TL;DR

This paper investigates the thermodynamic behavior of a scalar field model with momentum-dependent mass to understand confinement phenomena through positivity violation of propagators, analyzing potential inconsistencies and deconfinement signals.

Contribution

It introduces a scalar field model with nonlocal mass terms and studies its thermodynamics to explore confinement and positivity restoration at finite temperature.

Findings

Thermodynamic variables are derived from the model's partition function.

The study assesses the potential for positivity restoration indicating deconfinement.

The model's thermodynamic properties reveal insights into confinement mechanisms.

Abstract

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. 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, in order to study whether or not there is a restoration of positivity (hence, deconfinement, in our language).