Schrodinger Evolution for the Universe: Reparametrization

TL;DR

This paper introduces a new framework for defining and evolving observables in reparametrization-invariant theories, relaxing traditional constraints and distinguishing types of gauge symmetries to enable richer quantum gravity models.

Contribution

It proposes a novel class of observables called 'mutables' that generalize existing approaches and clarifies the physical interpretation of partial and complete observables.

Findings

Reveals a physical distinction between two types of gauge symmetries.

Explains non-unitary evolution as a limit breakdown.

Potential application to quantum gravity via Shape Dynamics.

Abstract

Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription for the observables of a totally constrained system (`perennials') and allows one to recover the influential partial and complete observables approach in a particular limit. Difficulties such as the non-unitary evolution of the complete observables in terms of certain partial observables are explained as a breakdown of this limit. Identification of our observables (`mutables') relies upon a physical distinction between gauge symmetries that exist at the level of histories and states (`Type 1'), and those that exist at the level of histories and not states (`Type 2'). This distinction resolves a tension in the literature concerning the physical interpretation of the partial observables and allows for a richer class of observables in the quantum theory. There is the potential for the application of our proposal to the quantization of gravity when understood in terms of the Shape Dynamics formalism.