Ultraviolet finiteness of Chiral Perturbation Theory for two-dimensional Quantum Electrodynamics

TL;DR

This paper demonstrates that in two-dimensional quantum electrodynamics, the chiral perturbation theory remains ultraviolet finite at all orders when reformulated in a bosonic framework, highlighting its consistency and finiteness.

Contribution

It reformulates 2D QED in a bosonic form and proves the all-order ultraviolet finiteness of the fermion mass perturbation theory.

Findings

Bosonic reformulation of 2D QED with exponential interaction.

Ultraviolet finiteness of boson Green's functions without vacuum loops.

All-order perturbative finiteness established in the bosonic framework.

Abstract

We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.