Weyl geometry in late 20th century physics

TL;DR

This paper surveys the resurgence of Weyl geometry in late 20th-century physics, highlighting its applications in gravity, quantum mechanics, particle physics, and cosmology, and discusses its ongoing research potential.

Contribution

It provides a comprehensive overview of Weyl geometry's renewed relevance in various physics domains during the late 20th century.

Findings

Weyl geometry was applied in scalar tensor theories of gravity.

It played a role in foundational physics, including gravity and quantum mechanics.

Weyl geometry shows ongoing research potential for physics foundations.

Abstract

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn from physical theory in the early 1920s. It had a comeback in the last third of the 20th century in different contexts: scalar tensor theories of gravity, foundations of physics (gravity, quantum mechanics), elementary particle physics, and cosmology. Here we survey the last two segments. It seems that Weyl geometry continues to have an open research potential for the foundations of physics after the turn of the century.