A Geometric Framework for Non-Kahler Complex Spacetime and Emergent Particle Dynamics

Abstract

We propose a speculative geometric framework in which the physical universe is modeledby a complex eight-dimensional spacetime consisting locally of four real and four imaginarycoordinates. The real and imaginary sectors are not assumed to be exactly orthogonal;instead, a small geometric misalignment parameter δ ≪ 1 measures their deviation from theidealized orthogonal complex structure. The resulting background is taken to be genericallynon-K¨ahler and to possess its own intrinsic dynamics.In this framework, matter is not introduced as a fundamental field. Instead, particlesare identified with stable periodic or limit-cycle structures of the underlying geometricdynamics. Their spectral data are conjectured to be related to periodic-orbit data throughtrace-formula-type relations. Mass, electric charge, weak isospin, and color are interpreted asdistinct geometric holonomies or accumulated geometric phases associated with translations,rotations, and local complex-frame twisting. The Lorentz group and the gauge groups areproposed to arise as structure-preserving subgroups of a larger automorphism structure ofthe complex geometry.The framework further proposes a geometric origin for quantum behavior, thermaltime, gravity, and several cosmological phenomena. It distinguishes global complex-modulidynamics from local periodic-orbit geometry. Teichm¨uller and Weil–Petersson geometryare reserved for the global cosmological sector, while Birkhoff normal forms and KAM-typeneighborhoods describe the local geometry near stable particle orbits.This document is a research framework rather than a completed physical theory. Thefundamental non-K¨ahler dynamical equations, the exact particle-spectrum map, the derivationof the Standard Model gauge groups, and quantitative experimental predictions remain open problems