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Quantum Geometry and Wild embeddings as quantum states

Nov, 2012
15 pages
Published in:
  • Int.J.Geom.Meth.Mod.Phys. 10 (2013) 1350055
  • Published: 2013
e-Print:
DOI:
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Abstract: (arXiv)
In this paper we discuss wild embeddings like Alexanders horned ball and relate them to fractal spaces. We build a C⋆C^{\star}-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 4-dimensional spacetime. We discuss the consequences for cosmology.
Note:
  • 16 pages, 4 figures
  • wild embeddings
  • Alexanders horned sphere
  • C*-algebras
  • deformation quantization
  • embedding
  • cosmological model
  • quantum geometry
  • quantization
  • algebra: C*
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