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A generalization of symmetrized density matrices in combination with thetechnique of generating functions allows to calculate the partition function ofidentical particles in a parabolic confining well. Harmonic two-bodyinteractions (repulsive or attractive) are taken into account. Also theinfluence of a homogeneous magnetic field, introducing anisotropy in the model,is examined. Although the theory is developed for fermions and bosons, specialattention is payed to the thermodynamic properties of bosons and theircondensation.Comment: 13 REVTEX pages + 9 postscript figure

Thermodynamics of coupled identical oscillators within the path-integral formalism