Canonical Commutator and Mass Renormalization
نویسنده
چکیده
The question considered is the effect on the canonical commutation rules of mass renormalization in quantum etectrodynamics. 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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