Topological Field Theory As The Key To Quantum Gravity

TL;DR

This paper explores a novel approach to quantum gravity by modeling the universe as a 3D topological quantum field theory, constructing states and a Hilbert space without path integrals, using tensor categories.

Contribution

It introduces a new framework connecting topological field theories with quantum gravity, avoiding path integrals through recombination diagrams in tensor categories.

Findings

Constructed propagating states for parts of the universe.

Developed a Hilbert space approximation for the universe.

Established a connection between TQFT and quantum gravity models.

Abstract

Motivated by the similarity between CSW theory and the Chern Simons state for General Relativity in the Ashtekar variables, we explore what the universe would look like if it were in a state corresponding to a 3D TQFT. We end up with a construction of propagating ststes for parts of the universe and a Hilbert space corresponding to a certain approximation. The construction avoids path integrals, using instead recombination diagrams in a certain tensor category.