OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY

TL;DR

This paper introduces the T-Theory, a generally covariant quantum field theory based on the loop representation, to explore quantum general relativity's consistency by calculating transition probabilities between volume eigenstates.

Contribution

It develops a tentative covariant quantum gravity model using loop variables and demonstrates explicit transition probability calculations, exploring foundational quantization choices.

Findings

Computed transition probability between volume eigenstates.

Discussed the impact of quantization choices on the theory.

Provided a framework for testing quantum general relativity.

Abstract

We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field; it is based on the loop representation, and on a certain number of quantization choices. Four-dimensional diffeomorphism-invariant quantum transition probabilities can be computed from the theory. We present the explicit calculation of the transition probability between two volume eigenstates as an example. We discuss the choices on which the T-theory relies, and the possibilities of modifying them.