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The unexpected resurgence of Weyl geometry in late 20-th century physics
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The unexpected resurgence of Weyl geometry in late 20-th century physics
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Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was withdrawn by its author from physical theorizing in the early 1920s.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.
Forward citations
Cited by 8 Pith papers
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Scale-invariant Schr\"{o}dinger geometry in symmetric teleparallel gravity
A quadratic nonmetricity action of Schrödinger type is locally scale-invariant exactly when its Palatini connection equations admit the length-preserving Schrödinger connection.
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Weyl gauge symmetry at LIGO-Virgo-KAGRA
In Weyl quadratic gravity linearized around de Sitter space, gravitational waves carry two tensor modes plus two transverse vector modes from the Weyl gauge field, with no scalar modes.
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Spontaneous Symmetry Breaking and the Emergent Einstein-Standard Model: From Weyl x SU (2)L x U (1)Y Gauge Theory to Geometric Mass Generation
Weyl x SU(2)L x U(1)Y gauge theory with quadratic curvature generates Einstein-Hilbert action, Higgs potential, and Standard Model masses via spontaneous Weyl symmetry breaking.
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Conformal symmetry, SM and Gravity
A Weyl-invariant SM+mirror-dark-matter+gravity model is developed via algebraic renormalization; its conformal cohomology is claimed trivial, and the required counterterms could — the author concedes not conclusively ...
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Jacobi stability of circular orbits around conformally invariant Weyl gravity black holes
Jacobi and Lyapunov stability of circular orbits around Weyl gravity black holes depends on the free parameters in the metric solutions.
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The fall and the rise of Weyl gauge theory
Weyl quadratic gauge gravity is anomaly-free, breaks via Stueckelberg to Einstein-Hilbert plus positive Lambda, and is the leading order of a regulator-free WDBI action that can include the SM.
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Weyl conformal geometry vs Riemannian geometry of Weyl gauge invariant dressed metric
Weyl geometry is equivalent to Riemannian geometry of a non-local dressed metric g*_{\mu\nu} via Wilson lines, with the quadratic and WDBI actions taking the same form in the symmetric phase.
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The fall and the rise of Weyl gauge theory
Weyl gauge theory of gravity is revived as the only anomaly-free gauge theory of spacetime symmetry with a physical gauge boson, exact geometric interpretation, all scales of geometric origin, and it generates the Ein...
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