Background Independent Quantum Mechanics and Gravity

TL;DR

This paper explores extending geometric quantum mechanics to incorporate background independence, proposing a quantum covariance framework and applying it to formulate a background independent Matrix Theory.

Contribution

It introduces a novel extension of geometric quantum mechanics with quantum covariance, aiming to achieve background independence in quantum gravity models.

Findings

Proposes a generalized geometric quantum mechanics framework.

Applies the framework to develop a background independent Matrix Theory.

Highlights the importance of quantum covariance for background independence.

Abstract

We argue that the demand of background independence in a quantum theory of gravity calls for an extension of standard geometric quantum mechanics. We discuss a possible kinematical and dynamical generalization of the latter by way of a quantum covariance of the state space. Specifically, we apply our scheme to the problem of a background independent formulation of Matrix Theory.