Topological geometrodynamics. III. Quantum theory

Journal Article · Wed Jan 01 04:00:00 EST 1986 · Int. J. Theor. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00669712· OSTI ID:7158308

Pitkanen, M

The description of 3-space as a spacelike 3-surface of the space H = M/sup 4/ x CP/sub 2/ (product of Minkowski space and two-dimensional complex projective space CP/sub 2/) and the idea that particles correspond to 3-surfaces of finite size in H are the basic ingredients of topological geometrodynamics, TGD, an attempt to a geometry-based unification of the fundamental interactions. The observations that the Schroedinger 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.

• Research Organization: Neste Oy Research Center, Kulloo
• OSTI ID: 7158308
• Journal Information: Int. J. Theor. Phys.; (United States), Journal Name: Int. J. Theor. Phys.; (United States) Vol. 25:1; ISSN IJTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSONS
CP INVARIANCE
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
GEOMETRY
INTERACTIONS
INVARIANCE PRINCIPLES
MAPPING
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
MATRICES
PARTICLE INTERACTIONS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
S MATRIX
SCALAR FIELDS
SPACE
SUPERSYMMETRY
SYMMETRY
SYMMETRY BREAKING
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGICAL MAPPING
TRANSFORMATIONS
UNIFIED-FIELD THEORIES