# On the Super-Renormalizablity of Quantum Gravity in the Linear Approximation

## TL;DR

This paper demonstrates that one-loop quantum gravity contributions in the linear approximation are trivial on physical states, suggesting potential simplifications for the broader problem of quantum gravity's renormalizability.

## Contribution

It proves that one-loop contributions in massless gravity are coboundaries, indicating a possible path to super-renormalizability in quantum gravity.

## Key findings

- One-loop contributions are coboundaries and vanish on physical states.
- The result may extend to higher orders, simplifying quantum gravity.
- Supports the conjecture of super-renormalizability in linear quantum gravity.

## Abstract

We compute the one-loop contributions of the chronological products for massless gravity in the second order of the perturbation theory. We prove that the loop contributions are coboundaries i.e. expressions which give zero when averaged on physical states. We conjecture that such a result should be true in higher orders of the perturbation theory also. This result should make easier the problem of constructive quantum field theory.