Weyl geometry in late 20th century physics

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Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn from physical theory in the early 1920s.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.

Draft paper to appear in V. Bach, D. Rowe (eds.) Beyond Einstein. Proceedings Mainz Conference September 2008. Einstein Studies. Basel: Birkhäuser

References in corpus (2)

• Cosmological spacetimes balanced by a scale covariant scalar field
• Dark Matter Halos as Bose-Einstein Condensates

Cited by in corpus (13)

• Weyl gauge symmetry and its spontaneous breaking in Standard Model and inflation
• Stueckelberg breaking of Weyl conformal geometry with applications to gravity
• Weyl $R^2$ inflation with an emergent Planck scale
• Transformation properties and general relativity regime in scalar-tensor theories
• Induced geometry from disformal transformation
• Length-preserving biconnection gravity and its cosmological implications
• Gravitational waves in conformal gravity
• Cosmology with vector distortion
• The unexpected resurgence of Weyl geometry in late 20-th century physics
• Solar-system tests of the inflation model with a Weyl term
• Behavior of vacuum and naked singularity under smooth gauge function in Lyra geometry
• Comparison of conformal gravitation theories by solutions analogous to Reissner-Nordström ones
• Quantum Geometrodynamics of Higher Derivative Theories with and without Conformal Symmetry