Topological higher gauge theory: From BF to BFCG theory

DOI10.1063/1.2888764zbMath1153.81366arXiv0708.3051OpenAlexW3099421892MaRDI QIDQ3544662

Eugeniu M. Popescu, Florian Girelli, Hendryk Pfeiffer

Publication date: 8 December 2008

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

Full work available at URL: https://arxiv.org/abs/0708.3051

Mathematics Subject Classification ID

Topological field theories in quantum mechanics (81T45) Topological quantum field theories (aspects of differential topology) (57R56)

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AKSZ models of semistrict higher gauge theory ⋮ Higher Chern-Simons based on (2-)crossed modules ⋮ Lorentzian quantum gravity via Pachner moves: one-loop evaluation ⋮ Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs ⋮ An invitation to higher gauge theory ⋮ Higher lattices, discrete two-dimensional holonomy and topological phases in (3 + 1)D with higher gauge symmetry ⋮ Perturbative BF theory ⋮ Dynamics of a lattice 2-group gauge theory model ⋮ Quantum geometry from higher gauge theory ⋮ On 3-gauge transformations, 3-curvatures, and Gray-categories ⋮ Dynamical generalization of Yetter's model based on a crossed module of discrete groups ⋮ Higher gauge theories based on 3-groups ⋮ Teleparallel gravity as a higher gauge theory ⋮ Hamiltonian analysis of the BFCG formulation of general relativity ⋮ Poincaré–Plebański formulation of GR and dual simplicity constraints ⋮ A 2-categorical state sum model ⋮ Topological invariant of 4-manifolds based on a 3-group ⋮ Gauge symmetry of the 3BF theory for a generic semistrict Lie three-group ⋮ Canonical formulation of Poincaré BFCG theory and its quantization

Cites Work

• P.l. homeomorphic manifolds are equivalent by elementary shellings
• 2-groups, trialgebras and their Hopf categories of representations
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• Spherical 2-categories and 4-manifold invariants
• Spherical categories
• Higher gauge theory and a non-abelian generalization of 2-form electrodynamics.
• Finite groups, spherical 2-categories, and 4-manifold invariants
• Diffeomorphisms and spin foam models
• Exactly soluble diffeomorphism invariant theories
• On \(C^1\)-complexes
• HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS
• Topological Quantum Field Theories from Homotopy n -Types
• Loop variables in topological gravity
• INTERPRETATIONS OF YETTER’S NOTION OF G-COLORING: SIMPLICIAL FIBRE BUNDLES AND NON-ABELIAN COHOMOLOGY
• Higher gauge theory—differential versus integral formulation
• TQFT’S FROM HOMOTOPY 2-TYPES
• STATE SUM CONSTRUCTION OF TWO-DIMENSIONAL OPEN-CLOSED TOPOLOGICAL QUANTUM FIELD THEORIES
• Scalar and tensorial topological matter coupled to (2 + 1)-dimensional gravity: I. Classical theory and global charges

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