Radiation reaction in quantum mechanics

The Lorentz-Dirac radiation reaction formula predicts that the position shift of a charged particle due to the radiation reaction is of first order in acceleration if it undergoes a small acceleration. A semi-classical calculation shows that this is impossible at least if the acceleration is due to a time-independent potential. Thus, the Lorentz-Dirac formula gives an incorrect classical limit in this situation. The correct classical limit of the position shift at the lowest order in acceleration is obtained by assuming that the energy loss at each time is given by the Larmor formula. 03.50.De, 12.20.-m Typeset using REVTEX e-mail address: [email protected] 1 A classical charge e with four-velocity u emits electromagnetic radiation with energymomentum P μ according to the Larmor formula: dP μ dτ = 2α 3 a u, (1) where τ is the proper time along the world line of the charge e and where a = √ −u̇μu̇μ (with u̇ = du/dτ) is the acceleration of the charge. (See, e.g., Ref. [1].) We have defined α = e/4π. It is widely believed that the radiation reaction is given by the Lorentz-Dirac formula [2,3]. The corresponding four-force K is given by K = 2α 3 (