Complete O(α) solution of the μ-decay problem

In this talk I report on the results of a complete O(\alpha) calculation of leptonic \mu-decay. The calculation is complete in the sense that all polarization and mass effects have been included in the radiative corrections. I mostly concentrate on the longitudinal polarization of the electron which considerably differs from the naive value P_e^l=-1 in the threshold region, both for the Born term and more so for the radiatively corrected case. I also discuss the role of the O(\alpha) anomalous spin-flip contribution and its description in terms of the equivalent particle approach which survives the m_e -> 0 limit. Finally, I provide a brief account of the history of the O(\alpha) radiative corrections to leptonic \mu-decay. I trace the error done in the first (wrong) 1956 calculation of Behrends, Finkelstein and Sirlin. My account of this historical error differs from that recently given in a talk by Kinoshita on the occasion of the 70th birthday of Sirlin.