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New Symmetry Principles in Quantum Field Theory (Paperback, Softcover reprint of the original 1st ed. 1992)
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New Symmetry Principles in Quantum Field Theory (Paperback, Softcover reprint of the original 1st ed. 1992)
Series: NATO Science Series B:, 295
Expected to ship within 10 - 15 working days
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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.
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