Charged scalars at finite electric field and temperature in the optimized perturbation theory

TL;DR

This paper investigates how a charged scalar field's symmetry behavior is affected by electric fields and temperature using optimized perturbation theory, revealing weak dependencies and phase transition changes.

Contribution

It provides analytical expressions for the effective potential under electric fields and temperature, and explores the nature of phase transitions in this context.

Findings

Weak decrease of vacuum expectation value with electric field and temperature

Transition from first-order to second-order phase transition under strong electric fields

Peak in vacuum persistence probability at the critical point, independent of coupling

Abstract

We study the symmetry breaking and restoration behavior of a self-interacting charged scalar field theory under the influence of a constant electric field and finite temperature. Our study is performed in the context of the optimized perturbation theory. The dependence of the effective potential with constant electric fields is established by means of the bosonic propagators in the Schwinger proper-time method. Explicit analytical expressions for the electric and thermal contributions are found. Our results show a very weak decreasing behavior of the vacuum expectation value as a function of the electric field, which is strengthened by the temperature effect. A first-order phase transition that occurs at zero/weak electric fields changes to a second-order phase transition under strong electric fields. The critical temperature for the phase transition exhibited a very weak dependence on the electric field. Additionally, we computed the vacuum persistence probability rate for the interacting theory, finding a peak at the critical point. The maximum value of this rate at the critical point is found to be independent of the coupling constant but depended solely on the magnitude of the electric field.