A Resummable beta-Function for Massless QED

TL;DR

The paper argues that in massless QED, the beta-function's perturbative series is resummable and free of nonperturbative power corrections within certain gauge-invariant renormalization schemes, clarifying its theoretical structure.

Contribution

It demonstrates that the beta-function in massless QED cannot have nonperturbative power corrections, ensuring its perturbative series is resummable within specific gauge-invariant frameworks.

Findings

Beta-function lacks nonperturbative power corrections.

Perturbative series for the beta-function is resummable.

Non-trivial fixed points are not implied by beta-function resummability.

Abstract

Within the set of schemes defined by generalized, manifestly gauge invariant exact renormalization groups for QED, it is argued that the beta-function in the four dimensional massless theory cannot possess any nonperturbative power corrections. Consequently, the perturbative expression for the beta-function must be resummable. This argument cannot be extended to flows of the other couplings or to the anomalous dimension of the fermions and so perturbation theory does not define a unique trajectory in the critical surface of the Gaussian fixed point. Thus, resummability of the beta-function is not inconsistent with the expectation that a non-trivial fixed point does not exist.