Functional integration of a nonrelativistic scalar field is an elegant formulation of
Quantum Field Theory to study the Thermodynamics of Bose-Einstein condensates,
made with dilute ultracold atomic gases.
In a beyond mean field approach one can derive the static and dynamical properties
of a condensate confined in different geometries and with D-spatial dimensions.
In particular, we have applied this method recently to calculate the condensate fraction
and the superfluid one of a dilute Bose-Einstein condensate in three and in two dimensions.
In another work, we have studied the condensation of an interacting Bose gas
confined on a thin spherical shell, a work triggered by the forthcoming experiments
with bubble traps in microgravity settings.