Phase Transition and Absence Of Ghosts in Rigid QED

TL;DR

This paper investigates a generalized form of QED with added world line curvature, revealing a phase transition and demonstrating that both phases are free of ghosts and tachyons due to quantum fluctuations.

Contribution

It introduces a phase transition in rigid QED and shows both phases are ghost-free, contrasting with classical higher derivative theories.

Findings

A phase transition exists in rigid QED with curvature.

Both phases are free of ghosts and tachyons.

Quantum fluctuations prevent classical pathologies.

Abstract

Ordinary QED formulated in the Feynman's space-time picture is equivalent to a one dimensional field theory. In the large N limit there is no phase transition in such a theory. In this letter, we show a phase transition does exist in a generalization of QED characterized by the addition of the curvature of the world line (rigidity) to the Feynman's space-time action. The large distance scale of the disordered phase essentially coincides with ordinary QED, while the ordered phase is strongly coupled. Although rigid QED exhibits the typical pathologies of higher derivative theories at the classical level, we show that both phases of the quantum theory are free of ghosts and tachyons. Quantum fluctuations prevent taking the naive classical limit and inherting the problems of the classical theory.