Fundamentals of Quantum Gravity

TL;DR

This paper presents a new approach to quantum gravity using affine variables, coherent states, and a projection operator method, offering fresh insights into nonrenormalizability and quantum constraints.

Contribution

It introduces novel affine-based techniques and a projection operator framework for quantum gravity, advancing the theoretical understanding of the field.

Findings

Development of affine kinematical variables

Introduction of affine coherent states

Application of projection operators to quantum constraints

Abstract

The outline of a recent approach to quantum gravity is presented. Novel ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach toward quantum constraints; (4) Continuous-time regularized functional integral representation without/with constraints; and (5) Hard core picture of nonrenormalizability. The ``diagonal representation'' for operator representations, introduced by Sudarshan into quantum optics, arises naturally within this program.