The book is based on the lectures given at the CIME school "Quantum
many body systems" held in the summer of 2010. It provides a
tutorial introduction to recent advances in the mathematics of
interacting systems, written by four leading experts in the field:
V. Rivasseau illustrates the applications of constructive Quantum
Field Theory to 2D interacting electrons and their relation to
quantum gravity; R. Seiringer describes a proof of Bose-Einstein
condensation in the Gross-Pitaevski limit and explains the effects
of rotating traps and the emergence of lattices of quantized
vortices; J.-P. Solovej gives an introduction to the theory of
quantum Coulomb systems and to the functional analytic methods used
to prove their thermodynamic stability; finally, T. Spencer
explains the supersymmetric approach to Anderson localization and
its relation to the theory of random matrices. All the lectures are
characterized by their mathematical rigor combined with physical
insights.
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