Thermodynamics of multi-boson phenomena

Using the method of locally equilibrium statistical operator we consider the thermalized relativistic quantum fields in an oscillatory trap. We compare this thermal picture of the confined boson gas with non-relativistic model of independent factorized sources. We find that they are equivalent in the limit of very large effective sizes $R$, more exactly, when the Compton wave length $1/m$ and thermal wave length $1/\sqrt{% mT}$ are much smaller than {\}$R$ . Under this conditions we study the influence of Bose condensation in finite volumes on the structure of the Wigner function, momentum spectra and correlation function.