A combinatorial approach to topological quantum field theories and invariants of graphs

DOI10.1007/BF02096773zbMath0768.57009MaRDI QIDQ1208031

Robert Schrader, Michael Karowski

Publication date: 16 May 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

quantum \(6j\)-symbolscoloured graphsbasis for the vector space of the topological quantum field theory associated to Riemann surfacecombinatorial state sum of Turaev and Viro for a compact 3-manifold

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Graph theory (05C99)

Related Items

Topological quantum field theory and invariants of graphs for quantum groups ⋮ Combinatorial quantization of the Hamiltonian Chern-Simons theory. I ⋮ Two dimensional lattice gauge theory based on a quantum group ⋮ Invariants of three-dimensional manifolds ⋮ State sum models with defects based on spherical fusion categories ⋮ A discrete approach to topological quantum field theories ⋮ State sum invariants of three-manifolds: A combinatorial approach to topological quantum field theories ⋮ Lattice topological field theory on nonorientable surfaces ⋮ Invariants of Three-Manifolds, Unitary Representations of the Mapping Class Group, and Numerical Calculations ⋮ Geometrical measurements in three-dimensional quantum gravity ⋮ Invariants of SPIN networks embedded in three-manifolds ⋮ Representation theory of Chern-Simons observables ⋮ On the relation between two quantum group invariants of 3-cobordisms ⋮ SPIN TOPOLOGICAL QUANTUM FIELD THEORIES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topological quantum field theories
• Fusion rules and modular transformations in 2D conformal field theory
• Topological gauge theories and group cohomology
• Topological quantum field theory
• Quantum field theory and the Jones polynomial
• Computer calculation of Witten's 3-manifold invariant
• On quantum gauge theories in two dimensions
• Conformal field theory and the cohomology of the moduli space of stable bundles
• Quasi-quantum groups, knots, three-manifolds, and topological field theory
• Ribbon graphs and their invariants derived from quantum groups
• Superselection sectors with braid group statistics and exchange algebras
• Axioms for Euclidean Green's functions
• Invariants of 3-manifolds via link polynomials and quantum groups
• On E. Verlinde’s Formula in the Context of Stable Bundles
• TOPOLOGICAL QUANTUM FIELD THEORIES FROM GENERALIZED 6J-SYMBOLS
• SOME EXAMPLES OF CRYSTALLOGRAPHIC GROUPS IN LOBAČEVSKIĬ SPACES
• A construction of topological quantum field theories from \(6j\)-symbols

This page was built for publication: A combinatorial approach to topological quantum field theories and invariants of graphs