A K\"{a}hler and quaternion-K\"{a}hler spacetime structure

TL;DR

The paper proposes that real Lorentzian spacetime may have an underlying pseudo-Kähler or pseudo-quaternion-Kähler structure, inspired by higher division algebra embeddings and symmetry considerations related to the standard model.

Contribution

It introduces the idea that spacetime could possess a pseudo-Kähler or pseudo-quaternion-Kähler structure derived from higher division algebra embeddings and symmetry constraints.

Findings

Quantum numbers resemble those of the standard model.

Spacetime may inherit symmetry constraints from a higher-dimensional ambient manifold.

Supports the geometric unification approach in theoretical physics.

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-K\"{a}hler or pseudo-quaternion-K\"{a}hler structure, real spacetime being a submanifold that inherits the symmetry contraints of the larger ambient manifold.