QED: Chiral transition and the issue of triviality

TL;DR

This paper reviews lattice QED studies, emphasizing analytical methods, bounds on critical exponents, and the non-triviality of QED, concluding that data supports non-Gaussian power law scaling.

Contribution

It provides a comprehensive review of lattice QED, derives bounds for critical exponents, and clarifies the non-trivial nature of QED through data analysis.

Findings

Triviality is ruled out on theoretical grounds.

Data supports power law scaling with non-Gaussian exponents.

Analytical methods are effective in data analysis.

Abstract

I give a review and progress report on studies of lattice QED. I emphasize analytical results and methods that are applied in data analysis. Also, I derive some bounds for the critical exponents and establish their connection with scaling violations. Triviality, as realized in $\phi^4$ theory, is ruled out on theoretical grounds. I show that the present data, if analyzed correctly, all lead to the same conclusions. They are compatible with power law scaling with nongaussian exponents.