Authors: Matti Pitkänen
Comments: 64 Pages.
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.
Category: Quantum Physics