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Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized toribbon categories which replace the category of representations of the gaugegroup. This provides a framework in which the gauge group becomes a quantumgroup while space-time is still given by the `classical' lattice. At thetechnical level, this construction generalizes the Spin Foam Model dual toLattice Gauge Theory and defines the partition function for a giventriangulation of a closed and oriented piecewise-linear 4-manifold. Thisdefinition encompasses both the standard formulation of d=4 pure Yang-Millstheory on a lattice and the Crane-Yetter invariant of 4-manifolds. Theconstruction also implies that a certain class of Spin Foam Models formulatedusing ribbon categories are well-defined even if they do not correspond to aTopological Quantum Field Theory.Comment: 41 pages, LaTeX, postscript/PiCTeX figures; v2:typos correcte

Four-dimensional lattice gauge theory with ribbon categories and the Crane–Yetter state sum