Abstract:
The recent status of Topological Geometrodynamics (TGD) is reviewed. One can end up with TGD either by starting from the energy problem of General Relativity or from the need to generalize hadronic or super string models. The basic principle of the theory is ’Do not quantize! ’ meaning that quantum physics is reduced to Kähler geometry and spinor structure of the infinite-dimensional space of 3-surfaces in 8dimensional space H = M 4 + × CP2 with physical states represented by classical spinor fields. General coordinate invariance implies that classical theory becomes an exact part of the quantum theory and configuration space geometry and that spacetime surfaces are generalized Bohr orbits. The uniqueness of the infinite-dimensional Kähler geometric existence fixes imbedding space and the dimension of the spacetime highly uniquely and implies that superconformal and supercanonical symmetries acting on the lightcone boundary δM 4 + × CP2 are cosmologies symmetries. The work with the p-adic aspects of TGD, the realization of the possible role of quaternions and octonions in the formulation of quantum TGD, the discovery of infinite
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