An Introduction to Renormalization in Atomic Physics
- URL: http://arxiv.org/abs/2204.02800v1
- Date: Tue, 29 Mar 2022 11:09:07 GMT
- Title: An Introduction to Renormalization in Atomic Physics
- Authors: Milan \v{S}indelka
- Abstract summary: We study quantum dynamics of a model of a nonrelativistic single electron atom coupled to the quantum radiation field.
An interaction between the electron and the radiation field is regularized, using a suitable cutoff prescription.
We identify the radiation reaction force acting on the electron, and show that this force actually diverges towards infinity when gradually removing the UV cutoff.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The purpose of these notes is to provide a pedagogical introduction to the
concept of renormalization in atomic physics. We study quantum dynamics of a
model of a nonrelativistic single electron atom coupled to the quantum
radiation field in the dipole approximation. An interaction between the
electron and the radiation field is regularized, using a suitable cutoff
prescription which eliminates the coupling of the electron to the highly
ultraviolet (UV) field modes. Subsequently, we analyze the corresponding
Heisenberg picture equations of motion, and focus on behavior of physical
observables in the limit of a pointlike electron (i.e., in the limit when the
above mentioned UV cutoff is gradually lifted to infinity). We identify the
radiation reaction force acting on the electron, and show that this force
actually diverges towards infinity when gradually removing the UV cutoff. Such
an analysis leads ultimately to an unique renormalization prescription for the
electron mass, as well as to determination of the Abraham-Lorentz force acting
on the electron. Dependence of the just sketched renormalization procedure upon
the spatial dimension is highlighted. Finally, we present an example
calculation of the atomic level shifts by means of the renormalized
perturbation theory, and formulate also the renormalized mean field theory.
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