Quantum Groups, Quantum Categories and Quantum Field TheoryThis book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students. |
Contents
Representation Theory of Ured sl₂ | 119 |
Path Representations of the Braid Groups for Quantum Groups | 141 |
Duality Theory for Local Quantum Theories Dimensions and Balancing | 176 |
3 other sections not shown
Other editions - View all
Quantum Groups, Quantum Categories and Quantum Field Theory Jürg Fröhlich,Thomas Kerler Limited preview - 2006 |
Quantum Groups, Quantum Categories and Quantum Field Theory Jurg Frohlich,Thomas Kerler No preview available - 2014 |
Common terms and phrases
0-category automorphism braid group braid statistics braided category braided tensor category C₁ Cat G cocycle commutes conformal field theories conjugation corresponding d₁ decomposition defined denote endomorphisms equivalent exists F-matrices formula functor fusion rule algebra fusionrules G₁ G₂ given grad Grad(Obj graded graphs H₁ Hence hexagonal equation highest weight Hopf algebra implies intertwiners invariant invertible objects involution irreducible objects irreducible representations isomorphism Lemma matrices monoidal category morphisms multiplication obtained Perron Frobenius proof properties Proposition q-dimensions quantum category quantum field theories quantum group quantum theory quotient rule algebra homomorphisms Section selfconjugate space space-like cones space-time stab(p statistical dimension statistical phases structure subgroup superselection sectors symmetric tensor categories tensor product Theorem trivial unique unitary representations V₁ V₂ vector W₁ Z₂