Huygens' principle - a synthetic account

TL;DR

This paper offers an axiomatic and synthetic framework for understanding Huygens' principle of wave fronts, using primitive notions like touching and a weak metric, simplifying previous complex expositions.

Contribution

It introduces a new axiomatic approach to Huygens' principle based on primitive notions, providing a simplified and synthetic perspective.

Findings

Provides an axiomatic foundation for Huygens' principle

Simplifies previous complex expositions of the principle

Uses primitive notions like touching and a weak metric

Abstract

We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. of Categories 32 (2017), 803-822