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-β0 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¯ anomalous dimension of the QED electron field depends on the gauge parameter only at one loop.