World of Classical Worlds

The topics of this chapter are the purely geometric aspects of the vision about physics as an infinite-dimensional Kahler geometry of configuration space or the "world of classical worlds"(WCW), with "classical world" identified either as 3-D surface of the unique Bohr orbit like 4-surface traversing through it. The non-determinism of Kahler action forces to generalize the notion of 3- surfaces so that unions of space-like surfaces with time like separations must be allowed. The considerations are restricted mostly to real context and the problems related to the p-adicization are discussed later.

There are two separate tasks involved.

1. Provide WCW with Kahler geometry which is consistent with 4-dimensional general coordinate invariance so that the metric is Diff4 degenerate. General coordinate invariance implies that the definition of metric must assign to a give 3-surface X³ a 4-surface as a kind of Bohr orbit X⁴(X³).

2. Provide the WCW with a spinor structure. The great idea is to identify WCW gamma matrices in terms of super algebra generators expressible using second quantized fermionic oscillator operators for induced free spinor fields at the space-time surface assignable to a given 3-surface. The isometry generators and contractions of Killing vectors with gamma matrices would thus form a generalization of Super Kac-Moody algebra.....

Keywords: Geometrization of physics, Kahler geometry, infinite dimensional geometry, isometry, symmetric space, super-conformal symmetries, Super Kac-Moody algebra, symplectic symmetry, spinor structure, second quantization, Killing vector fields, zero modes, Dirac action, Dirac equation.