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'Shape Dynamics': Foundations Reassessed
General Relativity and Quantum Cosmology · Submitted 13 May 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This points to changing conception of VPCTs from the current finite integral implementation to an infinitesimal differential implementation (or to avoiding using them at all).
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The abstract, sentence by sentence
`Shape dynamics' is meant here in the sense of a type of conformogeometrical reformulation of GR, some of which have of late been considered as generalizations of or alternatives to GR. This note concerns in particular cases based on the notion of volume-preserving conformal transformations (VPCTs), in the sense of preserving a solitary global volume of the universe degree of freedom. The extent to which various ways of modelling VPCTs make use of group theory at all, in a congruous manner, and with minimal departure from standard Lie group theory, is considered. This points to changing conception of VPCTs from the current finite integral implementation to an infinitesimal differential implementation (or to avoiding using them at all). Some useful observations from flat-space conformal groups (well-known from CFT) concerning the existence or otherwise of VPCT groups are also provided.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | `Shape dynamics' is meant here in the sense of a type of conformogeometrical reformulation of GR, some of which have of late been considered as generalizations of or alternatives to GR. | background 1.00 | 0.06 | 0.04 | asserted 0.80 |
| s1 | This note concerns in particular cases based on the notion of volume-preserving conformal transformations (VPCTs), in the sense of preserving a solitary global volume of the universe degree of freedom. | background 0.51 | 0.14 | 0.05 | asserted 0.95 |
| s2 | The extent to which various ways of modelling VPCTs make use of group theory at all, in a congruous manner, and with minimal departure from standard Lie group theory, is considered. | contribution 0.84 | 0.44 | 0.06 | unclear 0.61 |
| s3 | This points to changing conception of VPCTs from the current finite integral implementation to an infinitesimal differential implementation (or to avoiding using them at all). | contribution 0.36 | 0.35 | 0.42 | hedged possibility 0.64 |
| s4 | Some useful observations from flat-space conformal groups (well-known from CFT) concerning the existence or otherwise of VPCT groups are also provided. | contribution 0.62 | 0.52 | 0.07 | asserted 0.95 |
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The paper
Original abstract
`Shape dynamics' is meant here in the sense of a type of conformogeometrical reformulation of GR, some of which have of late been considered as generalizations of or alternatives to GR. This note concerns in particular cases based on the notion of volume-preserving conformal transformations (VPCTs), in the sense of preserving a solitary global volume of the universe degree of freedom. The extent to which various ways of modelling VPCTs make use of group theory at all, in a congruous manner, and with minimal departure from standard Lie group theory, is considered. This points to changing conception of VPCTs from the current finite integral implementation to an infinitesimal differential implementation (or to avoiding using them at all). Some useful observations from flat-space conformal groups (well-known from CFT) concerning the existence or otherwise of VPCT groups are also provided.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
What it cites · 8 sentences without a confident label
Cites as background 6 papers
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A number of relational models – in the Leibnizian [ref] and Machian [ref] senses of the word – are now available [ref] .
The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena · Introduction · 0.95
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A number of relational models – in the Leibnizian [ref] and Machian [ref] senses of the word – are now available [ref] .
Classical Machian Resolution of the Spacetime Reconstruction Problem · Introduction · 0.95
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A number of relational models – in the Leibnizian [ref] and Machian [ref] senses of the word – are now available [ref] .
A Shape Dynamics Tutorial · Introduction · 0.95
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