Causal evolution of spin networks

TL;DR

This paper introduces a novel quantum gravity framework combining loop quantum gravity and causal set theory, representing quantum states with spin networks and null edges, and explores its dynamics across various dimensions.

Contribution

It presents a new approach linking loop representation and causal sets, defining quantum amplitudes for spin network causal sets with dimension-specific models.

Findings

The theory exists in 3+1, 2+1, and 1+1 dimensions.

In 1+1 dimensions, the model relates to directed percolation, suggesting possible critical behavior.

The approach respects discrete causal structure and may have a classical limit.

Abstract

A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1+1 dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.