dorsal/arxiv
View Schema4-Dimensional BF Theory as a Topological Quantum Field Theory
| Authors | John C. Baez |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507006 |
| URL | https://arxiv.org/abs/q-alg/9507006 |
| DOI | 10.1007/BF00398315 |
| Journal | Lett.Math.Phys. 38 (1996) 129-143 |
Abstract
Starting from a Lie group G whose Lie algebra is equipped with an invariant nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory with cosmological term gives rise to a TQFT satisfying a generalization of Atiyah's axioms to manifolds equipped with principal G-bundle. The case G = GL(4,R) is especially interesting because every 4-manifold is then naturally equipped with a principal G-bundle, namely its frame bundle. In this case, the partition function of a compact oriented 4-manifold is the exponential of its signature, and the resulting TQFT is isomorphic to that constructed by Crane and Yetter using a state sum model, or by Broda using a surgery presentation of 4-manifolds.
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"abstract": "Starting from a Lie group G whose Lie algebra is equipped with an invariant\nnondegenerate symmetric bilinear form, we show that 4-dimensional BF theory\nwith cosmological term gives rise to a TQFT satisfying a generalization of\nAtiyah\u0027s axioms to manifolds equipped with principal G-bundle. The case G =\nGL(4,R) is especially interesting because every 4-manifold is then naturally\nequipped with a principal G-bundle, namely its frame bundle. In this case, the\npartition function of a compact oriented 4-manifold is the exponential of its\nsignature, and the resulting TQFT is isomorphic to that constructed by Crane\nand Yetter using a state sum model, or by Broda using a surgery presentation of\n4-manifolds.",
"arxiv_id": "q-alg/9507006",
"authors": [
"John C. Baez"
],
"categories": [
"q-alg",
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"doi": "10.1007/BF00398315",
"journal_ref": "Lett.Math.Phys. 38 (1996) 129-143",
"title": "4-Dimensional BF Theory as a Topological Quantum Field Theory",
"url": "https://arxiv.org/abs/q-alg/9507006"
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