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The virtues of resolvent algebras, compared to other approaches for thetreatment of canonical quantum systems, are exemplified by infinite systems ofnon-relativistic bosons. Within this framework, equilibrium states of trappedand untrapped bosons are defined on a fixed C*-algebra for all physicallymeaningful values of the temperature and chemical potential. Moreover, thealgebra provides the tools for their analysis without having to rely on 'adhoc' prescriptions for the test of pertinent features, such as the appearanceof Bose-Einstein condensates. The method is illustrated in case ofnon-interacting systems in any number of spatial dimensions and sheds new lighton the appearance of condensates. Yet the framework also covers interactionsand thus provides a universal basis for the analysis of bosonic systems.

Trapped bosons, thermodynamic limit and condensation: a study in the framework of resolvent algebras