Schrödinger Evolution for the Universe: Reparametrization

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We develop a new framework for constructing the quantum observables of theories invariant under global time reparametrizations. Our starting point is a generalised Hamilton-Jacobi formalism for totally constrained systems. Our end result is a quantum formalism which simultaneously preserves: i) genuine evolution; and ii) the constraint structure of the classical formalism in the semi-classical limit. We thus offer a novel resolution of the 'problem of time' for theories invariant under global time reparametrization. There is the potential for the application of our proposal to the quantization of gravity when understood in terms of the Shape Dynamics formalism.
Original languageEnglish
Article number065004
Number of pages26
JournalClassical and Quantum Gravity
Issue number6
Publication statusPublished - 23 Feb 2016

Structured keywords

  • Centre for Science and Philosophy


  • canonical quantum gravity
  • Hamilton-Jacobi theory
  • observables
  • problem of time
  • shape dynamics


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