Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-06-04
J.Math.Phys.42:5272-5305,2001
Physics
High Energy Physics
High Energy Physics - Theory
41 pages, LaTeX, postscript/PiCTeX figures; v2:typos corrected
Scientific paper
10.1063/1.1398063
Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized to ribbon categories which replace the category of representations of the gauge group. This provides a framework in which the gauge group becomes a quantum group while space-time is still given by the `classical' lattice. At the technical level, this construction generalizes the Spin Foam Model dual to Lattice Gauge Theory and defines the partition function for a given triangulation of a closed and oriented piecewise-linear 4-manifold. This definition encompasses both the standard formulation of d=4 pure Yang-Mills theory on a lattice and the Crane-Yetter invariant of 4-manifolds. The construction also implies that a certain class of Spin Foam Models formulated using ribbon categories are well-defined even if they do not correspond to a Topological Quantum Field Theory.
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