Quantum Physics


Quantum Hall Effect and Hierarchy of Planck Constants

Authors: Matti Pitkänen

I have already earlier proposed the explanation of FQHE, anyons, and fractionization of quantum numbers in terms of hierarchy of Planck constants realized as a generalization of the imbedding space H = M4 x CP2 to a book like structure. The book like structure applies separately to CP2 and to causal diamonds (CD ⊂ M4) defined as intersections of future and past directed light-cones. The pages of the Big Book correspond to singular coverings and factor spaces of CD (CP2) glued along 2-D subspace of CD (CP2) and are labeled by the values of Planck constants assignable to CD and CP2 and appearing in Lie algebra commutation relations. The observed Planck constant h, whose square defines the scale of M4 metric corresponds to the ratio of these Planck constants. The key observation is that fractional filling factor results if h is scaled up by a rational number. In this chapter I try to formulate more precisely this idea. The outcome is a rather detailed view about anyons on one hand, and about the Kähler structure of the generalized imbedding space on the other hand.

Comments: 64 Pages.

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Submission history

[v1] 15 Dec 2008
[v2] 21 Dec 2008
[v3] 2012-01-30 22:44:04

Unique-IP document downloads: 178 times

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