Feynman diagrams of generalized matrix models and the associated manifolds in dimension four. (English) Zbl 0971.81101
Summary: The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which rely on the interplay between ideas from physics and from advanced mathematics. On the mathematical side, a central role is played by combinatorial topology, often used to recover the space-time manifold from the other structures involved. An extremely attractive possibility is that of encoding all possible space-times as specific Feynman diagrams of a suitable field theory. In this work we analyze how exactly one can associate combinatorial four-manifolds with the Feynman diagrams of certain tensor theories.
MSC:
| 81T18 | Feynman diagrams |
| 81T45 | Topological field theories in quantum mechanics |
| 83C45 | Quantization of the gravitational field |
| 58D30 | Applications of manifolds of mappings to the sciences |
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