The unexpected resurgence of Weyl geometry in late 20-th century physics

Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s.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 gravity, foundations of quantum mechanics, elementary particle physics, and cosmology. It seems that Weyl geometry continues to offer an open research potential for the foundations of physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep 2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur

Topological Quantum Groups, Star Products and their relations

. This short summary of recent developments in quantum compact groups and star products is divided into 2 parts. In the first one we recast star products in a more abstract form as deformations and review its recent developments. The second part starts with a rapid presentation of standard quantum group theory and its problems, then moves to their completion by introduction of suitable Montel topologies well adapted to duality. Preferred deformations (by star products and unchanged coproducts) of Hopf algebras of functions on compact groups and their duals, are of special interest. Connection with the usual models of quantum groups and the quantum double is then presented. 0 - INTRODUCTION. The idea that quantum theories are deformations of classical theories was presumably in the back of the mind of many scientists, even before the mathematical notion of deformation was formalized by Gerstenhaber [G] for algebraic structures. We were even told by witnesses (many of whom contribute..