Anomalous Dimension of Dirac's Gauge-Invariant Nonlocal Order Parameter in Ginzburg-Landau Field Theory

Abstract

In a Ginzburg-Landau theory with $n$ fields, the anomalous dimension of the gauge-invariant nonlocal order parameter defined by the long-distance limit of Dirac's gauge-invariant two-point function is calculated. The result is exact for all $n$ to first order in $\epsilon \equiv 4-d$, and for all $d\in (2,4)$ to first order in $1/n$, and coincides with the previously calculated gauge-dependent exponent in the Landau gauge.