TY - BOOK ID - 216129 TI - Quantum Spaces : Poincaré Seminar 2007 AU - Rivasseau, Vincent. AU - Poincaré Seminar AU - Poincaré Seminar PY - 2007 SN - 1281180432 9786611180430 3764385227 3764385219 PB - Basel : Birkhäuser Basel : Imprint: Birkhäuser, DB - UniCat KW - Noncommutative differential geometry KW - Quantum Hall effect KW - Space and time KW - Quantum theory KW - Differential geometry, Noncommutative KW - Geometry, Noncommutative differential KW - Non-commutative differential geometry KW - Infinite-dimensional manifolds KW - Operator algebras KW - Quantum theory. KW - Quantum Physics. KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Physics KW - Mechanics KW - Thermodynamics KW - Quantum physics. UR - https://www.unicat.be/uniCat?func=search&query=sysid:216129 AB - This book starts with an introduction by V. Pasquier on the usefulness of non-commutative geometry, especially in the condensed matter context of the Hall effect. This theme is further developed by A. Polychronakos, who together with L. Susskind introduced the concept of non-commutative fluids. Jean-Michel Maillet compares the experimental results on one dimensional magnetic chains to the theoretical predictions based on the algebraic Bethe Ansatz and related to quantum group symmetries that he actively developed with many collaborators. On the high energy side of non-commutative geometry the ER -