Fakeons, quantum gravity and the correspondence principle

TL;DR

This paper proposes an upgraded correspondence principle incorporating fakeons, leading to a unique, renormalizable, and unitary quantum gravity theory in four dimensions, expanding the framework of quantum field theory.

Contribution

It introduces a modified correspondence principle that includes fakeons, enabling the construction of a unique quantum gravity theory that is both renormalizable and unitary.

Findings

A fakeon of spin 2 and a scalar field achieve renormalizability and unitarity in 4D quantum gravity.

The upgraded principle refines unitarity, locality, and renormalizability to accommodate quantum gravity.

The approach offers a comprehensive overview of particles and fakeons across various dimensions.

Abstract

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity.