Purely virtual extension of quantum field theory for gauge invariant fields: quantum gravity

TL;DR

This paper introduces a purely virtual extension to quantum gravity that enables the definition of gauge-invariant, point-dependent observables and their off-shell correlations without affecting on-shell physics, ensuring unitarity and gauge independence.

Contribution

It proposes a novel purely virtual cloud sector extension to quantum gravity, allowing gauge-invariant observables and off-shell correlation functions while maintaining unitarity and physical consistency.

Findings

One-loop two-point functions are positive and gauge independent.

Off-shell correlation functions are well-defined and unaffected by the extension.

The approach preserves unitarity and the optical theorem in quantum gravity.

Abstract

Quantum gravity is extended to include purely virtual "cloud sectors", which allow us to define a complete set of point-dependent observables, including a gauge invariant metric and gauge invariant matter fields, and calculate their off-shell correlation functions perturbatively. The ordinary on-shell correlation functions and the $S$ matrix elements are unaffected. Each extra sector is made of a cloud field, its anticommuting partner, a "cloud-fixing" function and a cloud Faddeev-Popov determinant. The additional fields are purely virtual, to ensure that no ghosts propagate. The extension is unitary. In particular, the off-shell, diagrammatic version of the optical theorem holds. The one-loop two-point functions of dressed scalars, vectors and gravitons are calculated. Their absorptive parts are positive, cloud independent and gauge independent, while they are unphysical if non purely virtual clouds are used. We illustrate the differences between our approach to the problem of finding a complete set of observables in quantum gravity and other approaches available in the literature.