The Unexpected Resurgence of Weyl Geometry in late 20th-Century Physics

DOI10.1007/978-1-4939-7708-6_11zbMath1402.83012arXiv1703.03187OpenAlexW2611537337MaRDI QIDQ4557064

Erhard Scholz

Publication date: 29 November 2018

Published in: Einstein Studies (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.03187

zbMATH Keywords

Riemannian geometryWeyl geometry

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Geometrodynamics and the holographic principle (83E05) Applications of differential geometry to physics (53Z05) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) History of relativity and gravitational theory (83-03)

Related Items (14)

A classification of global conformal invariants ⋮ Induced geometry from disformal transformation ⋮ Unweyling three mysteries of Nordström gravity ⋮ Weyl-ambient geometries ⋮ Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential ⋮ Projective transformations in metric-affine and Weylian geometries ⋮ Light cone and Weyl compatibility of conformal and projective structures ⋮ The Plasticine Ball Argument ⋮ Gravitational waves in conformal gravity ⋮ Weyl \(R^2\) inflation with an emergent Planck scale ⋮ A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection ⋮ Unfolding conformal geometry ⋮ A link that matters: towards phenomenological tests of unimodular asymptotic safety ⋮ Weyl relativity: a novel approach to Weyl's ideas

Cites Work

• MOND-like acceleration in integrable Weyl geometric gravity
• Weyl gauge-vector and complex dilaton scalar for conformal symmetry and its breaking
• Derivation of the Dirac equation by conformal differential geometry
• Making the case for conformal gravity
• Editorial note to: J. Ehlers, F. A. E. Pirani and A. Schild, ``The geometry of free fall and light propagation
• Supersymmetric gauged scale covariance in ten and lower dimensions
• Interpretation of quantum nonlocality by conformal quantum geometrodynamics
• Towards a theory of spacetime theories. Based on the presentations of a conference at the Interdisciplinary Centre for Science and Technology Studies, IZWT, Wuppertal, Germany, July 21--23, 2010
• Proof of the spin-statistics theorem
• Varying gravity. Dirac's legacy in cosmology and geophysics
• A Weyl-Dirac cosmological model with DM and DE
• Geometric realizations, curvature decompositions, and Weyl manifolds
• Cosmologies with varying speed of light: a historical perspective
• Conformal symmetry and the standard model
• Relativistic quantum mechanics and the Bohmian interpretation
• A new improved energy-momentum tensor.
• On dark energy, Weyl's geometry, different derivations of the vacuum energy density and the pioneer anomaly
• The Noether theorems. Invariance and conservation laws in the twentieth century. Transl. from the French by Bertram E. Schwarzbach
• Quantification géométrique.
• Beyond Einstein gravity. A survey of gravitational theories for cosmology and astrophysics.
• Cosmological spacetimes balanced by a Weyl geometric scale covariant scalar field
• Wave fields in Weyl spaces and conditions for the existence of a preferred pseudo-Riemannian structure
• Characterization of standard clocks by means of light rays and freely falling particles
• Consistency of Weyl's geometry as a framework for gravitation
• Geometric quantization and quantum mechanics
• Fiber bundle techniques in gauge theories. Lectures in mathematical physics at the University of Texas at Austin. Edited by A. Böhm and J. D. Dollard
• Conformally coupled dark matter
• Some remarks on the genesis of scalar-tensor theories
• Newton's first law revisited
• On the history of unified field theories
• Three-dimensional Einstein-Weyl geometry
• On the relation of Weyl geometry and Bohmian quantum mechanics
• The conformal transformation's controversy: what are we missing?
• Between two disciplines. B. L. van der Waerden and the development of quantum mechanics
• Why Einstein did not believe that general relativity geometrizes gravity
• The construction of the Higgs mechanism and the emergence of the electroweak theory
• Wyl manifolds
• On Weyl's Gauge Field
• On Weyl's Gauge Field. II
• Dynamical string tension in string theory with spacetime Weyl invariance
• Proof of the spin-statistics theorem in the relativistic regimen by Weyl’s conformal quantum mechanics
• The renormalization group and Weyl invariance
• A modified variational principle for gravity in the modified Weyl geometry
• General relativity and Weyl geometry
• High precision thermal modeling of complex systems with application to the flyby and Pioneer anomaly
• Weyl geometric gravity and electroweak symmetry “breaking”
• Weyl's scale invariance for the standard model, renormalizability and the zero cosmological constant
• A Cyclic Model of the Universe
• Isotropic cosmologies in Weyl geometry
• Constraints on the nature of inertial motion arising from the universality of free fall and the conformal causal structure of space-time
• Invariant Theoretical Interpretation of Interaction
• Lorentz Invariance and the Gravitational Field
• Mach's Principle and a Relativistic Theory of Gravitation
• THE STUECKELBERG FIELD
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• Constructive axiomatic approach to spacetime torsion
• Observer fields in Weylian spacetime models
• Establishing the Riemannian structure of space-time by means of light rays and free matter waves
• ON THE GENERAL COVARIANCE IN BOHMIAN QUANTUM GRAVITY
• ON THE GEOMETRIZATION OF BOHMIAN MECHANICS: A NEW APPROACH TO QUANTUM GRAVITY
• The role of the internal metric in generalized Kaluza–Klein theories
• The Scalar-Tensor Theory of Gravitation
• Constraint algebra and equations of motion in the Bohmian interpretation of quantum gravity
• NONMINIMAL SCALAR–TENSOR THEORIES AND QUANTUM GRAVITY
• QUANTUM, GRAVITY AND GEOMETRY
• About Some Problems Raised by the Relativistic Form of De-Broglie–Bohm Theory of Pilot Wave
• CONFORMAL SCALING GAUGE SYMMETRY AND INFLATIONARY UNIVERSE
• Variational and conformal structure of nonlinear metric-connection gravitational Lagrangians
• A gauge theory of the Weyl group
• Gravitational theory in Weyl integrable spacetime
• GENERAL RELATIVITY AND WEYL FRAMES
• GEOMETRIZED INSTANTONS AND THE CREATION OF THE UNIVERSE
• Gauge Theories of Gravitation
• The intrinsic helicity of elementary particles and the spin-statistic connection
• Zero rest-mass fields including gravitation: asymptotic behaviour
• General relativity with spin and torsion: Foundations and prospects
• Multivalued Fields
• On the embedding of space-time in five-dimensional Weyl spaces
• Quantization and unitary representations
• Lagrangian Density for Perfect Fluids in General Relativity
• Mach's Principle and Invariance under Transformation of Units
• Electroweak scale invariant models with small cosmological constant
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• Ricci-Calculus
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Unexpected Resurgence of Weyl Geometry in late 20th-Century Physics