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Recurrence and explicit formulae for contractions (partial traces) ofantisymmetric and symmetric products of identical trace class operators arederived. Contractions of product density operators of systems of identicalfermions and bosons are proved to be asymptotically equivalent to,respectively, antisymmetric and symmetric products of density operators of asingle particle, multiplied by a normalization integer. The asymptoticequivalence relation is defined in terms of the thermodynamic limit ofexpectation values of observables in the states represented by given densityoperators. For some weaker relation of asymptotic equivalence, concerning thethermodynamic limit of expectation values of product observables, normalizedantisymmetric and symmetric products of density operators of a single particleare shown to be equivalent to tensor products of density operators of a singleparticle.  This paper presents the results of a part of the author's thesis [W. Radzki,"Kummer contractions of product density matrices of systems of $n$ fermions and$n$ bosons" (Polish), MS thesis, Institute of Physics, Nicolaus CopernicusUniversity, Toru\'{n}, 1999].

Contractions of product density operators of systems of identical fermions and bosons