A monoidal representation for linearized gravity

TL;DR

This paper introduces a novel monoidal representation for linear quantum gravity, utilizing a commutative monoid structure similar to electromagnetism's loop representation, enabling duality generators and geometric insights.

Contribution

It presents a new mathematical framework for linear quantum gravity based on monoids, differing from traditional group-based approaches, and discusses its geometric interpretation.

Findings

Realizes the duality generator within the new representation

Provides a geometric interpretation of the monoidal structure

Establishes a foundation for alternative quantum gravity models

Abstract

We propose an alternative representation for linear quantum gravity. It is based on the use of a structure that bears some resemblance to the Abelian loop representation used in electromagnetism but with the difference that space of extended object on which waves functions take values have a structure of commutative monoid instead of Abelian group. The generator of duality of the theory is realized in this representation and a geometrical interpretation is discussed.