Manifestly gauge invariant QED

TL;DR

This paper introduces a gauge-invariant calculation method for QED that avoids fixing the gauge or specifying regularisation, using integration by parts and gauge identities within an exact renormalisation group framework.

Contribution

It presents a novel diagrammatic and gauge-invariant approach to QED calculations that does not require gauge fixing or regularisation details.

Findings

One-loop beta function calculated without gauge fixing.

Method yields universal results.

Calculations performed diagrammatically.

Abstract

We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. Calculations can be performed almost entirely diagrammatically. The method is formulated within the framework of an exact renormalisation group for QED. We demonstrate the technique with a calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing.