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Quantum Spaces
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Quantum Spaces

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ISBN-13:
9783764385224
Einband:
Ebook
Seiten:
227
Autor:
Vincent Rivasseau
Serie:
53, Progress in Mathematical Physics
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:

"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.
Quantum Hall Effect and Non-commutative Geometry.- Non-commutative Renormalization.- Non-commutative Fluids.- Heisenberg Spin Chains: From Quantum Groups to Neutron Scattering Experiments.- Non-commutative Geometry and the Spectral Model of Space-time.
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 book includes two complementary reviews. A. Connes describes the striking progress recently made in gathering all the interactions and fields of the standard model into a non-commutative geometry on a simple internal space, while V. Rivasseau describes in a large review the very recent technique of renormalization of quantum field theories on non-commutative space-time, which lead to the surprising discovery of their improved short-distance behavior.