QED out of matter

TL;DR

This paper demonstrates how certain non-renormalizable models with current-current interactions can be fine-tuned to behave like QED at low energies, illustrating the universality of the Wilsonian renormalization group.

Contribution

It shows how to tune parameters in simple models without gauge fields to replicate QED behavior at low energies, highlighting the universality of renormalization.

Findings

Models can be tuned to match QED at low energies

Non-renormalizable interactions can be effectively renormalized

Wilsonian RG applies to models without elementary gauge fields

Abstract

The Wilsonian renormalization group implies that an arbitrary four dimensional field theory with an ultraviolet cutoff is equivalent to a theory which is renormalizable by power counting at energy scales much below the cutoff. This applies to any theory including those with non-renormalizable interactions as long as we fine-tune the mass parameters. We analyze two simple models with current-current interactions but without elementary gauge fields from this viewpoint. We show how to tune the parameters of the models so that they become equivalent to QED at energies much below the cutoff.