136 Citations
The Unexpected Resurgence of Weyl Geometry in late 20th-Century Physics
- Physics
- 2017
Weyl’s original scale geometry of 1918 (“purely infinitesimal geometry”) was withdrawn by its author from physical theorizing in the early 1920s. It made a surprising comeback, however, in the last…
A Curvature Identity on a 4-Dimensional Riemannian Manifold
- Mathematics
- 2010
We recall a curvature identity for 4-dimensional compact Riemannian manifolds as derived from the generalized Gauss–Bonnet formula. We extend this curvature identity to non-compact 4-dimensional…
On Cosymplectic Conformal Connections
- Mathematics
- 2021
The aim of this paper is to introduce a cosymplectic analouge of conformal connection in a cosymplectic manifold and proved that if cosymplectic manifold M admits a cosymplectic conformal connection…
Singularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose
- PhysicsFoundations of Physics
- 2021
In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity…
Gauging the Spacetime Metric—Looking Back and Forth a Century Later
- Physics
- 2019
H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local scale gauge (later called {\em Weyl geometry}) was motivated by mathematical, philosophical and physical considerations. It…
The Changing Faces of the Problem of Space in the Work of Hermann Weyl
- PhysicsStudies in History and Philosophy of Science
- 2019
During his life Weyl approached the problem of space (PoS) from various sides. Two aspects stand out as permanent features of his different approaches: the unique determination of an affine…
Gravitation and cosmology with York time
- Physics
- 2016
[Shortened abstract:] In this thesis we investigate a solution to the `problem of time' in canonical quantum gravity by splitting spacetime into surfaces of constant mean curvature parameterised by…
Quantum mechanics as the dynamical geometry of trajectories
- Physics
- 2015
We illustrate how non-relativistic quantum mechanics may be recovered from a dynamical Weyl geometry on configuration space and an `ensemble' of trajectories (or `worlds'). The theory, which is free…