Non-equilibrium scalar fields at finite temperature and density

Abstract

We study propagators in bosonic field theories at finite temperature and chemical potential using the Schwinger-Keldysh real-time formalism. The system is considered in contact with a thermal reservoir, allowing for a consistent treatment of both equilibrium and non-equilibrium situations. The chemical potential, associated with conserved charges, modifies the structure of the propagators and introduces features that require detailed analysis. We focus on how a finite chemical potential affects the analytic structure of the bosonic propagators, including changes in the position of poles and the structure of branch cuts. In our setup, the chemical potential enters the theory as a constant background field, which alters both the dynamics and the boundary conditions. This work provides a basis for understanding the behavior of bosonic fields in thermal and dense environments.