Pure shape dynamics: General framework

Abstract

We put forward a general framework for describing relational physical theories, which we call Pure Shape Dynamics (PSD). Elaborating on the original insights brought about by the Shape Dynamics program, PSD's novel take on relationalism is its insistence on describing any dynamical system by means of the intrinsic geometry of its associated curve in the suitable relational configuration space of the theory, namely shape space, whereby the corresponding equation of state of the curve expresses the ratio of change of one of its geometric degrees of freedom with respect to another one. The mathematical structure underlying the equation of state is a local section over a natural generalization of the unit tangent bundle, which we call shape phase space.

arXiv comment25 pages. Published in Classical and Quantum Gravity

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Cited by in corpus (7)

• Herglotz Action for Homogeneous Cosmology
• A Proposal for a Metaphysics of Self-Subsisting Structures. I. Classical Physics
• A de Broglie-Bohm Model of Pure Shape Dynamics: $N$-body system
• Shape space as a conceptual space
• A proposal for a metaphysics of self-subsisting structures. II. Quantum physics
• Pure shape dynamics, self-subsisting structures, and the nature of time
• General Relativity and Background Independence