Foundations of Physics 43 (12):1428-1458 (2013)

Tim Koslowski
University of Würzburg
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
Keywords Shape dynamics  General relativity  Canonical formalism  Conformal methods  Initial value problem
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DOI 10.1007/s10701-013-9754-0
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Leibnizian Relationalism for General Relativistic Physics.Antonio Vassallo & Michael Esfeld - 2016 - Studies in History and Philosophy of Modern Physics:101-107.
Quantum Inflation of Classical Shapes.Tim Koslowski - 2017 - Foundations of Physics 47 (5):625-639.

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