QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories

TL;DR

This paper demonstrates that four-dimensional canonical Lorentzian quantum gravity naturally regularizes matter quantum field theories, making the Hamiltonian of the standard model finite without renormalization, akin to string theory but within a non-perturbative framework.

Contribution

It shows that quantum gravity can serve as a natural regulator for matter quantum field theories, providing a non-perturbative, finite Hamiltonian for the standard model.

Findings

Hamiltonian supports dense operators with Wilson loops and fermionic/Higgs insertions

Hamiltonian is finite without renormalization

Shared properties with string theory in a specific phase

Abstract

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized.