From Quantum Gravity to Quantum Field Theory via Noncommutative Geometry

TL;DR

This paper establishes a connection between quantum gravity and quantum field theory using noncommutative geometry, showing how fermionic fields and interactions emerge from a spectral triple framework in semi-classical limits.

Contribution

It introduces a spectral triple approach that links quantum gravity states to fermionic quantum field theories, revealing how classical fields and interactions arise from quantum geometric structures.

Findings

Semi-classical states yield interacting fermions in gravitational fields.

Turning off gravity results in free fermionic quantum field theory.

Flux tubes mediate interactions between fermions and gravity.

Abstract

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The interaction involves flux tubes of the gravitational field. In the additional limit where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges.