dorsal/arxiv
View SchemaTopological Interpretations of Lattice Gauge Field Theory
| Authors | Doug Bullock, Charles Frohman, Joanna Kania-Bartoszyńska |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710003 |
| URL | https://arxiv.org/abs/q-alg/9710003 |
| DOI | 10.1007/s002200050471 |
| Journal | Commun.Math.Phys. 198 (1998) 47-81 |
Abstract
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that are not distinguishable by observables. We prove that when the quantum group is a deformation of a connected algebraic group (over the complex numbers), then the algebra of observables forms a deformation quantization of the ring of characters of the fundamental group of the lattice with respect to the corresponding algebraic group. Finally, we investigate lattice gauge field theory based on quantum SL(2,C), and conclude that the algebra of observables is the Kauffman bracket skein module of a cylinder over a surface associated to the lattice.
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"abstract": "We construct lattice gauge field theory based on a quantum group on a lattice\nof dimension 1. Innovations include a coalgebra structure on the connections,\nand an investigation of connections that are not distinguishable by\nobservables. We prove that when the quantum group is a deformation of a\nconnected algebraic group (over the complex numbers), then the algebra of\nobservables forms a deformation quantization of the ring of characters of the\nfundamental group of the lattice with respect to the corresponding algebraic\ngroup. Finally, we investigate lattice gauge field theory based on quantum\nSL(2,C), and conclude that the algebra of observables is the Kauffman bracket\nskein module of a cylinder over a surface associated to the lattice.",
"arxiv_id": "q-alg/9710003",
"authors": [
"Doug Bullock",
"Charles Frohman",
"Joanna Kania-Bartoszy\u0144ska"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/s002200050471",
"journal_ref": "Commun.Math.Phys. 198 (1998) 47-81",
"title": "Topological Interpretations of Lattice Gauge Field Theory",
"url": "https://arxiv.org/abs/q-alg/9710003"
},
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