Fakeons And Lee-Wick Models

TL;DR

This paper studies fakeon models, which include nonphysical degrees of freedom to ensure unitarity and renormalizability in higher-derivative theories, with implications for quantum gravity.

Contribution

It formulates fakeon models via nonanalytic Wick rotation and proves their perturbative unitarity and renormalizability, clarifying their properties and potential in quantum gravity.

Findings

Fakeon models are perturbatively unitary to all orders.

Models are renormalizable if power counting constraints are met.

Average continuation matches nonanalytic Wick rotation predictions.

Abstract

The "fakeon" is a fake degree of freedom, i.e. a degree of freedom that does not belong to the physical spectrum, but propagates inside the Feynman diagrams. Fakeons can be used to make higher-derivative theories unitary. Moreover, they help us clarify how the Lee-Wick models work. In this paper we study the fakeon models, that is to say the theories that contain fake and physical degrees of freedom. We formulate them by (nonanalytically) Wick rotating their Euclidean versions. We investigate the properties of arbitrary Feynman diagrams and, among other things, prove that the fakeon models are perturbatively unitary to all orders. If standard power counting constraints are fulfilled, the models are also renormalizable. The S matrix is regionwise analytic. The amplitudes can be continued from the Euclidean region to the other regions by means of an unambiguous, but nonanalytic, operation, called average continuation. We compute the average continuation of typical amplitudes in four, three and two dimensions and show that its predictions agree with those of the nonanalytic Wick rotation. By reconciling renormalizability and unitarity in higher-derivative theories, the fakeon models are good candidates to explain quantum gravity.