Quantum geometry with intrinsic local causality

TL;DR

This paper develops a background independent, locally causal quantum spacetime model using labeled 2-surfaces, incorporating discrete geometric features and holographic principles, extending quantum general relativity.

Contribution

It introduces a novel framework replacing spin networks with labeled 2-surfaces, defining a new state space and dynamics for quantum spacetime with causal structure.

Findings

The theory satisfies the Bekenstein bound.

The holographic hypothesis is reformulated within this formalism.

Constructs histories with discrete spacetime geometry features.

Abstract

The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional surfaces. The space of states of the theory is the direct sum of the spaces of invariant tensors of a quantum group G_q over all compact (finite genus) oriented 2-surfaces. The dynamics is background independent and locally causal. The dynamics constructs histories with discrete features of spacetime geometry such as causal structure and multifingered time. For SU(2) the theory satisfies the Bekenstein bound and the holographic hypothesis is recast in this formalism.