A primordial theory
arXiv:cond-mat/0401015
Abstract
We review the twistor approach to the Zhang-Hu theory of the four-dimensional Quantum Hall effect. We point out the key role played by the group Spin(4,4), as the symmetry group of the boundary. It is argued that this group, which ignores the square root of minus one used in relativity and quantum mechanics, is the focal point of a primordial theory, one where the Cartan concept of triality is paramount, from which the standard theories emerge via a series of phase transitions of the Zhang-Hu fluid. An important role will be played by the Jordan cross-product algebras, particularly the exceptional Jordan algebra associated to the split octaves and by the associated Freudenthal phase space. The geometry and Hamiltonian theory of these spaces is examined in detail. A possible link to the theory of massive particles is outlined.
55 pages
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