  In this work the Klein-Gordon (KG) equation for a complex scalar field with
U(1) symmetry endowed in a mexican-hat scalar field potential with thermal and
electromagnetic contributions is written as a Gross-Pitaevskii (GP)-like
equation. This equation is interpreted as a charged generalization of the GP
equation at finite temperatures found in previous works. Its hydrodynamical
representation is obtained and the corresponding thermodynamical properties are
derived and related to measurable quantities. The condensation temperature in
the non-relativistic regime associated with the aforementioned system within
the semiclassical approximation is calculated. Also, a generalized equation for
the conservation of energy for a charged bosonic gas is found when
electromagnetic fields are introduced, and it is studied how under certain
circumstances its breaking of symmetry can give some insight on the phase
transition of the system not just into the condensed phase but also on other
related systems.
