Line geometry and electromagnetism I: basic structures

TL;DR

This paper explores the connection between line geometry and electromagnetism, demonstrating how fundamental structures in pre-metric electromagnetism can be understood through line geometry concepts, with results summarized in a comprehensive table.

Contribution

It introduces a novel interpretation of electromagnetism's basic structures using line geometry, bridging geometric concepts with physical theories.

Findings

Most pre-metric electromagnetism structures correspond to line geometry concepts

Key notions of line geometry are applicable to mechanics and electromagnetism

Results are systematically summarized in a comparative table

Abstract

Some key notions of line geometry are recalled, along with their application to mechanics. It is then shown that most of the basic structures that one introduces in the pre-metric formulation of electromagnetism can be interpreted directly in terms of corresponding concepts in line geometry. The results are summarized in a table.