Rivasseau, V., Seiringer, R., Solovej, J.P., Spencer, Th.
Giuliani, Alessandro, Mastropietro, Vieri, Yngvason, Jakob (Eds.)
2012, XIII, 180 p. 11 illus., 1 illus. in color.
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Tutorial presentation of advanced topics introduces the reader to some of the most exciting topics of modern mathematical physics Examples and physical applications guide the reader towards a deep comprehension of sophisticated mathematical tools Serves as a guide through recent literature on the mathematics of interacting fermionic and bosonic systems
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.
Content Level »Research
Keywords »82B10; 81V70; 82B28; 82B44 - Interacting Fermi and Bose systems - Mathematical physics - Quantum many body problem - Quantum statistical mechanics