The constraints of post-quantum classical gravity

Abstract

We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and phase-space density. The theory can either be considered fundamental or as an effective theory where the classical limit is taken of space-time. The theories have the dynamics of general relativity as their classical limit and provide a way to study the back-action of quantum fields on the space-time metric. The theory is invariant under spatial diffeomorphisms, and here, we provide a methodology to derive the constraint equations of such a theory by imposing invariance of the dynamics under time-reparametrization invariance. This leads to generalisations of the Hamiltonian and momentum constraints. We compute the constraint algebra for a wide class of realisations of the theory (the "discrete class") in the case of a quantum scalar field interacting with gravity. We find that the algebra doesn't close without additional constraints, although these do not necessarily reduce the number of local degrees of freedom.

32 +4 pages, V2 added background material and general improvements. Accepted in JHEP

References in corpus (7)

• Quantum Gravity at a Lifshitz Point
• A Spin Entanglement Witness for Quantum Gravity
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Scale invariance, unimodular gravity and dark energy
• Foundations and Measures of Quantum Non-Markovianity
• Loop Quantum Gravity: An Inside View
• Hybrid classical-quantum formulations ask for hybrid notions

Cited by in corpus (3)

• Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity
• Objective trajectories in hybrid classical-quantum dynamics
• A healthier semi-classical dynamics