Quantum geometry and wild embeddings as quantum states. (English) Zbl 1278.81116
Summary: In this paper, we discuss wild embeddings like Alexanders horned ball and relate them to fractal spaces. We build a \(C^{\ast}\)-algebra corresponding to a wild embedding. We argue that a wild embedding is the result of a quantization process applied to a tame embedding. Therefore, quantum states are directly the wild embeddings. Then we give an example of a wild embedding in the four-dimensional spacetime. We discuss the consequences for cosmology.
MSC:
| 81S10 | Geometry and quantization, symplectic methods |
| 53D55 | Deformation quantization, star products |
| 46L60 | Applications of selfadjoint operator algebras to physics |
| 57M30 | Wild embeddings |
| 28A80 | Fractals |
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