Models for Discrete Quantum Gravity

TL;DR

This paper introduces a framework for discrete quantum gravity using quantum sequential growth processes, analyzing their properties and providing methods for constructing concrete models.

Contribution

It develops a formal framework for discrete quantum processes and introduces quantum sequential growth processes with explicit construction methods.

Findings

The set of q-probability operators is convex with identifiable extreme points.

A property of consistency for discrete quantum processes is established.

Two methods for constructing models of quantum sequential growth processes are presented.

Abstract

We first discuss a framework for discrete quantum processes (DQP). It is shown that the set of q-probability operators is convex and its set of extreme elements is found. The property of consistency for a DQP is studied and the quadratic algebra of suitable sets is introduced. A classical sequential growth process is "quantized" to obtain a model for discrete quantum gravity called a quantum sequential growth process (QSGP). Two methods for constructing concrete examples of QSGP are provided.