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Shech's Argument for FQHE Requires EXACT 2D.md

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Shech's argument for FQHE Requires EXACT 2D
FQHE
02efc391-fd46-4d2e-84e2-e191e90cc0c7
20210701200812
20210316141305

Shech's argument (as I see it) for why the FQHE (or more specifically the observation of FQ stats) requires the configuration space of electrons to be exactly 2D

  1. FQHE shows/is compatible with/makes plausible the existence of [[fractional quantum statistics is the study of anyons]], i.e. the particles having an exchange factor of $e^{i2\pi\alpha}\quad \alpha\neq 0,1$
  2. The quantum statistics of a particle is determined by the 1D representation of its [[fundamental group]]
  3. The 1D representation of [[braid group]] is $e^{i2\pi\alpha}\quad\alpha\neq0,1$
  4. The Braid group is the fundamental group only of exchange in 2D space, as worldlines get entangled then.

$\therefore$ In order to explain anyons/FQHE, the configuration space of the electrons needs to be exactly 2D, not small 3D.