Perturbative Gravity in the Causal Approach

TL;DR

This paper develops a quantum theory of gravity using the causal approach, demonstrating gauge invariance and renormalizability up to second order, and explores interactions with matter and gauge fields, highlighting quantum-specific modifications.

Contribution

It provides a rigorous second-order perturbative quantum gravity framework within the causal approach, including matter and gauge interactions, with novel insights into quantum corrections.

Findings

Proves gauge invariance and renormalizability up to second order.

Identifies quantum modifications to classical energy-momentum tensor.

Introduces ghost terms necessary for consistent quantum interactions.

Abstract

Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system (massless and massive). Then we investigate the interaction of massless gravity with matter (described by scalars and spinors) and massless Yang-Mills fields. We obtain a difference with respect to the classical field theory due to the fact that in quantum field theory one cannot enforce the divergenceless property on the vector potential and this spoils the divergenceless property of the usual energy-momentum tensor. To correct this one needs a supplementary ghost term in the interaction Lagrangian.