On the Triviality of Textbook Quantum Electrodynamics

TL;DR

This paper investigates the triviality of lattice Quantum Electrodynamics (QED) by adding a four-fermion interaction, demonstrating that the theory is logarithmically trivial and supporting the idea that perturbative QED would vanish without a cutoff.

Contribution

It provides a high-precision lattice study showing that textbook QED with multiple fermion species is logarithmically trivial, confirming longstanding theoretical predictions.

Findings

QED exhibits a second order chiral phase transition.

Logarithmic triviality modifies mean field scaling laws.

Results support Landau's hypothesis of complete screening in QED.

Abstract

By adding a small, irrelevant four fermi interaction to the action of lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. This allows an ab initio high precision, controlled study of the existence of "textbook" Quantum Electrodynamics with several species of fermions. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial. The logarithms of triviality, which modify mean field scaling laws, are pinpointed in several observables. The result supports Landau's contention that perturbative QED suffers from complete screening and would have a vanishing fine structure constant in the absence of a cutoff.