Matching heavy-quark fields in QCD and HQET at three loops

The relation between the heavy-quark field in QCD and the corresponding field in HQET is derived up to three loops, and to all orders in the large-beta(0) limit. The corresponding relation between the QED electron field and the Bloch-Nordsieck one is gauge invariant to all orders. We also prove that the (MS) over bar anomalous dimension of the QED electron field depends on the gauge parameter only at one loop. (C) 2010 Elsevier B.V. All rights reserved.