**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 = M^{4} x CP_{2}
to a book like structure. The book like structure applies separately to CP_{2}
and to causal diamonds (CD ⊂ M^{4}) 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 (CP_{2}) glued along 2-D subspace of
CD (CP_{2}) and are labeled by the values of Planck constants assignable to
CD and CP_{2} and appearing in Lie algebra commutation relations. The
observed Planck constant h, whose square defines the scale of M^{4} 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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[v1] 15 Dec 2008

[v2] 21 Dec 2008

[v3] 2012-01-30 22:44:04

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