Topological geometrodynamics. III: Quantum theory
type: Item
instance of: scholarly article
title: Topological geometrodynamics. III: Quantum theory
zbMATH Open document ID: 0624.53053
DOI: 10.1007/BF00669712
author: Matti Pitkänen
published in: International Journal of Theoretical Physics
publication date: 1986-01-01T00:00:00Z
review text: [For parts I and II see ibid. 24, 775-821 (1985; Zbl 0601.53074), and ibid. 24, 823-871 (1985; Zbl 0601.53075).] The description of 3-space as a spacelike 3-surface of the space \(H=M^ 4\times CP_ 2\) (product of Minkowski space and two-dimensional complex projective space \(CP_ 2)\) and the idea that particles correspond to 3- surfaces of finite size in H are the basic ingredients of topological geometrodynamics, an attempt to a geometry-based unification of the fundamental interactions. The observations that the Schrödinger equation can be derived from a variational principle and that the existence of a unitary S matrix follows from the phase symmetry of this action lead to the idea that quantum TGD should be derivable from a quadratic phase symmetric variational principle in the space SH, consisting of the spacelike 3-surfaces of H. In this paper a formal realization of this idea is proposed. First, the space SH is endowed with the necessary geometric structures (metric, vielbein, and spinor structures) induced from the corresponding structures of the space H. Second, the concepts of the scalar super field in SH (both fermions and bosons should be describable by the same probability amplitude) and of super d'Alambertian are defined. It is shown that the requirement of a maximal symmetry leads to a unique CP-breaking super d'Alambertian and thus to a unique theory ``predicting everything''. Finally, a formal expression for the S matrix of the theory is derived.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83E05
Mathematics Subject Classification ID: 81T60
zbMATH DE Number: 4013491
zbMATH Keywords: Minkowski space
zbMATH Keywords: complex projective space
zbMATH Keywords: topological geometrodynamics
zbMATH Keywords: super field
zbMATH Keywords: super d'Alambertian
zbMATH Keywords: CP-breaking
MaRDI profile type: Publication
cites work: Q5530857
cites work: \(\mathbb{C} P^2\) as a gravitational instanton
cites work: Topological geometrodynamics
full work available at URL: https://doi.org/10.1007/bf00669712
OpenAlex ID: W2049114043
description: scientific article; zbMATH DE number 4013491