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Topological Geometrodynamics
Author(s) -
Pitkänen M.
Publication year - 1988
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19885000310
Subject(s) - physics , minkowski space , canonical quantization , string theory , topological quantum field theory , quantization (signal processing) , n = 4 supersymmetric yang–mills theory , topology (electrical circuits) , theoretical physics , mathematical physics , quantum mechanics , quantum , quantum gravity , mathematics , relationship between string theory and quantum field theory , algorithm , combinatorics
The identification of spacetime as a 4‐surface in the space H = M 4 ×CP 2 (product of Minkowski space and complex projective space of complex dimension two) as means of obtaining Poincare invariant theory of gravitation was the triggering idea of topological geometrodynamics (TGD), which can be regarded as an attempt to unify basic interactions in terms of submanifold geometry instead of abstract manifold geometry as in case of General Relativity. One can however regard TGD also as a generalization of string model: instead of strings free particles are regarded as 3‐surfaces. In this article I want to describe these two approaches and to show how they merge into a single coherent scheme provided macroscopic 3‐space with matter is identified as a 3‐surface containing particles as topological inhomogenities. Also the quantization program of TGD based on the idea that interacting field theory can be regarded as a classical, free field theory for Grassmann algebra valued Schrödinger amplitude in the space of all possible 3‐surfaces of H , is described.