The question considered is the effect on the canonical commutation rules of mass renormalization in quantum electrodynamics. This is investigated by considering the quantum Langevin equation for a charged quantum oscillator interacting with the radiation field via dipole interaction. Explicit expressions for the commutator are obtained for finite cutoff frequency as well as the large-cutoff limit. The surprising result obtained is that the exactly equal-time (canonical) commutator involves the bare mass, while the corresponding commutator for infinitesimally displaced times involves the renormalized mass. © 1989 Plenum Publishing Corporation.
Publication Source (Journal or Book title)
Journal of Statistical Physics
Ford, G., & O'Connell, R. (1989). Canonical commutator and mass renormalization. Journal of Statistical Physics, 57 (3-4), 803-810. https://doi.org/10.1007/BF01022833