2012/11/30 by Henrique Gomes, H. Gomes, Tim Koslowski +1 · 46 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Doubly special relativity #Four-force #Gauge theory #General relativity #Geometry #Introduction to gauge theory #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Symmetry (geometry) #Theoretical physics #Theory of relativity #gr-qc
paper · pdf · doi:10.1007/s10701-013-9754-0
published in Foundations of Physics 43(12), 1428-1458 (Springer Science+Business Media) · 22 pages
openalex publication_date 2013/11/04 · arxiv created 2013/11/30 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General Relativity can indeed be formulated as the dynamics of shapes. This new Shape Dynamics theory, unlike earlier proposals by Barbour and his collaborators, implements local spatial conformal invariance as a gauge symmetry that replaces refoliation invariance in General Relativity. It is the purpose of this paper to answer frequent questions about (new) Shape Dynamics, such as its relation to Poincaré invariance, General Relativity, Constant Mean (extrinsic) Curvature gauge, earlier Shape Dynamics, and finally the conformal approach to the initial value problem of General Relativity. Some of these relations can be clarified by considering a simple model: free electrodynamics and its dual shift symmetric formulation. This model also serves as an example where symmetry trading is used for usual gauge theories.