Pure shape dynamics: General framework

关于从关系形状动力学中涌现的光锥可能性

On the possibility of emergent light cones from relational shape dynamics

该研究通过关系形状动力学探讨了光锥速度的涌现机制，揭示了因果结构和最大信号速度可能由几何和谱性质动态产生。

Shape Dynamics in 2+1 Dimensions

Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. In this paper we explicitly construct Shape Dynamics for a torus universe in 2+1 dimensions through a linking gauge theory that ensures dynamical equivalence with General Relativity. The Hamiltonian we obtain is formally a reduced phase space Hamiltonian. The construction of the Shape Dynamics Hamiltonian on higher genus surfaces is not explicitly possible, but we give an explicit expansion of the Shape Dynamics Hamiltonian for large CMC volume. The fact that all…

Loop Quantization of Shape Dynamics

Loop Quantum Gravity (LQG) is a promising approach to quantum gravity, in particular because it is based on a rigorous quantization of the kinematics of gravity. A difficult and still open problem in the LQG program is the construction of the physical Hilbert space for pure quantum gravity. This is due to the complicated nature of the Hamilton constraints. The Shape Dynamics description of General Relativity (GR) replaces the Hamilton constraints with spatial Weyl constraints, so the problem of finding the physical Hilbert space reduces to the problem of quantizing the Weyl constraints. Unfort…

Observable Equivalence between General Relativity and Shape Dynamics

In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with General Relativity observables, whose observables can now be interpreted as particular representative functions of observables of a conformal theory at fixed York time. An application of the observable equivalence of General Relativity and Shape Dynamics is to define the quantization of General Relativity through quantizing Shape Dynamics and using observab…

Shape Dynamics. An Introduction

Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle configurations are dynamical. In the case of Riemannian three-geometries, the only dynamical variables are the parts of the metric that determine angles. The local scale factor plays no role. This leads to a shape-dynamic theory of gravity in which the four-dimensional diffeomorphism invariance of general relativity is replaced by three-dimensional diffeomor…

Linking shape dynamics and loop quantum gravity

Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation related to the Ashtekar variables by beginning with a modification of the Plebanski action. The constraints of shape dynamics and their algebra are reproduced in terms of these new variables.

Shape Dynamics and Gauge-Gravity Duality

The dynamics of gravity can be described by two different systems. The first is the familiar spacetime picture of General Relativity, the other is the conformal picture of Shape Dynamics. We argue that the bulk equivalence of General Relativity and Shape Dynamics is a natural setting to discuss familiar bulk/boundary dualities. We discuss consequences of the Shape Dynamics description of gravity as well as the issue why the bulk equivalence is not explicitly seen in the General Relativity description of gravity.