The Wilson exact renormalization group equation and the anomalous dimension parameter

TL;DR

This paper compares the original non-linear approach to the anomalous dimension in the Wilson exact renormalization group equation with current linear methods, highlighting differences in the construction of the flow equation.

Contribution

It provides a simple expression for the exactly marginal redundant operator derived from the non-linear approach, contrasting it with the linear case.

Findings

Non-linear approach yields a simple expression for the marginal operator.

Linear approach requires solving first-order differential equations.

The role of the redundant operator in flow equation construction is clarified.

Abstract

The non-linear way the anomalous dimension parameter has been introduced in the historic first version of the exact renormalization group equation is compared to current practice. A simple expression for the exactly marginal redundant operator proceeds from this non-linearity, whereas in the linear case, first order differential equations must be solved to get it. The role of this operator in the construction of the flow equation is highlighted.