dorsal/arxiv
View SchemaReflections on Topological Quantum Field Theory
| Authors | Roger Picken |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9707002 |
| URL | https://arxiv.org/abs/q-alg/9707002 |
| DOI | 10.1016/S0034-4877(97)85927-7 |
| Journal | Rept.Math.Phys. 40 (1997) 295-303 |
Abstract
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum Field Theory (TQFT) and to consider a modification of TQFT, applicable to embedded manifolds. After an introduction based around a simple example (Section 1) the notion of a d-dimensional TQFT is defined in category-theoretical terms, as a certain type of functor from a category of d-dimensional cobordisms to the category of vector spaces (Section 2). A construction due to Turaev, an operator-valued invariant of tangles, is discussed in Section 3. It bears a strong resemblance to 1-dimensional TQFTs, but carries much richer structure due to the fact that the 1-dimensional manifolds involved are embedded in a 3-dimensional space. This leads us, in Section 4, to propose a class of TQFT-like theories, appropriate to embedded, rather than pure, manifolds.
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"abstract": "(Talk presented at the XVth Workshop on Geometric Methods in Physics,\nQuantizations, Deformations and Coherent States, in Bialowieza, Poland, July\n1-7, 1996.) The aim of this article is to introduce some basic notions of\nTopological Quantum Field Theory (TQFT) and to consider a modification of TQFT,\napplicable to embedded manifolds. After an introduction based around a simple\nexample (Section 1) the notion of a d-dimensional TQFT is defined in\ncategory-theoretical terms, as a certain type of functor from a category of\nd-dimensional cobordisms to the category of vector spaces (Section 2). A\nconstruction due to Turaev, an operator-valued invariant of tangles, is\ndiscussed in Section 3. It bears a strong resemblance to 1-dimensional TQFTs,\nbut carries much richer structure due to the fact that the 1-dimensional\nmanifolds involved are embedded in a 3-dimensional space. This leads us, in\nSection 4, to propose a class of TQFT-like theories, appropriate to embedded,\nrather than pure, manifolds.",
"arxiv_id": "q-alg/9707002",
"authors": [
"Roger Picken"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1016/S0034-4877(97)85927-7",
"journal_ref": "Rept.Math.Phys. 40 (1997) 295-303",
"title": "Reflections on Topological Quantum Field Theory",
"url": "https://arxiv.org/abs/q-alg/9707002"
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