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We provide a quantum field theoretical derivation of theAbraham-Lorentz-Dirac (ALD) equation, describing the motion of an electricpoint charge sourcing an electromagnetic field, which back-reacts on the chargeas a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equationdescribing the motion of a point mass with self-force interacting with thelinearized metric perturbations caused by the mass off an otherwise vacuouscurved background spacetime. We regularize the formally divergent self-force bysmearing the direct part of the retarded Green's function and using aquasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevinequations with a classical stochastic force accounting for the effect of thequantum fluctuations in the field, which causes small fluctuations on theparticle trajectory. These equations will be useful for studying the stochasticmotion of charges and small masses under the influence of both quantum andclassical noise sources, derived either self-consistently or put in by handphenomenologically. We also show that history-dependent noise-induced driftmotions could arise from such stochastic sources on the trajectory that couldbe a hidden feature of gravitational wave forms hitherto unknown.Comment: 18 pages, 1 figure, submitted to PR

Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space