Tree Level Gravity - Scalar Matter Interactions in Analogy with Fermi Theory of Weak Interactions using Only a Massive Vector Field

TL;DR

This paper develops an effective model for scalar matter interactions in quantum gravity, analogous to Fermi theory, simplifying complex interactions into two main Lagrangians and confirming low-energy consistency.

Contribution

It introduces a novel effective model extending the I.T.B framework to gravity coupled with scalar matter, simplifying interaction series into manageable Lagrangians.

Findings

Rewrites infinite graviton-scalar interactions using two Lagrangians.

Low energy limit reproduces standard scalar-gravity coupling.

Demonstrates a new analogy between gravity interactions and Fermi theory.

Abstract

In this paper we work in perturbative Quantum Gravity coupled to Scalar Matter at tree level and we introduce a new effective model in analogy with the Fermi theory of weak interaction and in relation with a previous work where we have studied only the gravity and its self-interaction. This is an extension of the I.T.B model (Intermediate-Tensor-Boson) for gravity also to gravitational interacting scalar matter. We show that in a particular gauge the infinite series of interactions containing "n" gravitons and two scalars could be rewritten in terms of only two Lagrangians containing a massive field, the graviton and, obviously, the scalar field. Using the S-matrix we obtain that the low energy limit of the amplitude reproduce the local Lagrangian for the scalar matter coupled to gravity.