Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics

TL;DR

This paper explores Weyl geometry's role in understanding space-time topology, electromagnetic potentials, and particle physics, proposing a new perspective where particles are topological defects and spacetime is fundamentally 3D with dynamic spatial relations.

Contribution

It introduces a novel interpretation of elementary particles as topological defects within Weyl geometry and suggests spacetime is a 3D structure with evolving spatial relations.

Findings

Spinless electron and photon are topological defects.

Statistical and fluctuating metrics offer a new view of Maxwell equations.

Physical geometry is an approximation to mathematical geometry.

Abstract

Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and fluctuating metric in 3D space with time as a measure of spatial relations are discussed to propose a statistical interpretation of Maxwell field equations. It is argued that physical geometry is an approximation to mathematical geometry, and 4D relativistic spacetime is essentially 3D space with changing spatial relations. The present work is suggested to have radical new outlook on elementary particle physics.