Study of symmetry breaking of charged scalar field: Hydrodynamic version

TL;DR

This paper reformulates the Klein-Gordon equation for a charged scalar field into a Gross-Pitaevskii-like equation at finite temperature, deriving its hydrodynamic form and thermodynamics, including a generalized first law for charged BECs.

Contribution

It introduces a finite temperature generalization of the Gross-Pitaevskii equation for a charged scalar field and derives its hydrodynamic and thermodynamic properties.

Findings

Derived a new GP-like equation for charged scalar fields at finite temperature

Obtained the hydrodynamic version and thermodynamics of the charged scalar field

Formulated a generalized first law for charged Bose-Einstein Condensates

Abstract

We rewrite the Klein-Gordon (KG) equation for a complex scalar field as a new Gross-Pitaevskii (GP)-like equation. The potential of the scalar field is a mexican-hat potential and the field is in a thermal bath with one loop contribution. We interpret the new GP equation as a finite temperature generalization of the GP equation for a charged field. We find its hydrodynamic version as well and using it, we derive the corresponding thermodynamics. We also obtain a generalized first law for a charged Bose-Einstein Condensate (BEC).