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.
