Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Kähler and quaternion-Kähler spacetime structure

R. Vilela Mendes

Abstract

When real Lorentzian spacetime is embedded into a manifold parametrized by higher division algebras (complex or quaternion with Hermitean metric) and the representation constraints of their symmetry groups are made compatible, a set of quantum numbers is generated that is evocative of those of the standard model of particle physics. This is taken here as a hint that in spacetime there is a pseudo-Kähler or pseudo-quaternion-Kähler structure, real spacetime being a submanifold that inherits the symmetry contraints of the larger ambient manifold.

A Kähler and quaternion-Kähler spacetime structure

Abstract

When real Lorentzian spacetime is embedded into a manifold parametrized by higher division algebras (complex or quaternion with Hermitean metric) and the representation constraints of their symmetry groups are made compatible, a set of quantum numbers is generated that is evocative of those of the standard model of particle physics. This is taken here as a hint that in spacetime there is a pseudo-Kähler or pseudo-quaternion-Kähler structure, real spacetime being a submanifold that inherits the symmetry contraints of the larger ambient manifold.

Paper Structure

This paper contains 3 sections, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Universe as a local pseudo-Kähler manifold
  3. The quaternion-Kähler structure

Figures (1)

  • Figure 1: Penrose-like diagram for complex de Sitter spacetime. Horizontal planes (red) are complex 3-spheres and longitudinal lines (blue) complex 2-spheres. Light rays propagate on planes at 45 degrees