Abstract
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.
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Ford, G.W., O'Connell, R.F. Canonical commutator and mass renormalization. J Stat Phys 57, 803–810 (1989). https://doi.org/10.1007/BF01022833
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DOI: https://doi.org/10.1007/BF01022833