Particles, fields and a canonical distance form

TL;DR

This paper explores how the existence of elementary particles in classical physics relates to the topological properties of space-time, particularly when influenced by a Weyl field and a canonical distance form.

Contribution

It introduces a novel perspective linking elementary particles to non-trivial homotopy in space-time with Weyl field-generated metric relations.

Findings

Non-trivial homotopy can naturally arise in certain space-times.

Weyl fields influence the metric relations of space-time.

Implications for the understanding of elementary particles in classical physics.

Abstract

We examine a notion of an elementary particle in classical physics and suggest that its existence requires non-trivial homotopy of space-time. We show that non-trivial homotopy may naturally arise for space-times in which metric relations are generated by a canonical distance form factorized by a Weyl field. Some consequences of the presence of a Weyl field are discussed.