Quantum Stability of the Phase Transition in Rigid QED

TL;DR

This paper investigates the quantum stability of a phase transition in rigid QED, demonstrating that the transition persists after considering first quantum corrections, thus supporting its robustness.

Contribution

It provides the first analysis of quantum corrections to the phase transition in rigid QED, confirming its stability beyond leading order approximations.

Findings

The phase transition in rigid QED survives first quantum corrections.

Both phases remain free of ghosts and tachyons after corrections.

Quantum fluctuations do not eliminate the phase transition.

Abstract

Rigid QED is a renormalizable generalization of Feynman's space-time action characterized by the addition of the curvature of the world line (rigidity). We have recently shown that a phase transition occurs in the leading approximation of the large N limit. The disordered phase essentially coincides with ordinary QED, while the ordered phase is a new theory. We have further shown that both phases of the quantum theory are free of ghosts and tachyons. In this letter, we study the first sub-leading quantum corrections leading to the renormalized mass gap equation. Our main result is that the phase transition does indeed survive these quantum fluctuations.