New Symmetry Principles in Quantum Field Theory

J. Frölich

ISBN 10: 1461365384 / ISBN 13: 9781461365389

Published by Springer US, Springer US Okt 2012, 2012

About this Item

Neuware -Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a 'trivial representation' of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such 'Quantum Symmetries' was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 540 pp. Englisch.

Seller Inventory # 9781461365389

Bibliographic Details

• Title: New Symmetry Principles in Quantum Field Theory
• Publisher: Springer US, Springer US Okt 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 1461365384
• ISBN 13: 9781461365389
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 29D millimeters 254 millimeters width by 178 millimeters height by 29 millimeters depth
• Weight: 1003 grams

About this title

Synopsis

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad­ vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al­ gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par­ ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte­ grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.