Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics
- URL: http://arxiv.org/abs/2112.05613v1
- Date: Fri, 10 Dec 2021 15:48:24 GMT
- Title: Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics
- Authors: Roberto Passante, Lucia Rizzuto
- Abstract summary: We consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit.
These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we consider some second-order effective Hamiltonians
describing the interaction of the quantum electromagnetic field with atoms or
molecules in the nonrelativistic limit. Our procedure is valid only for
off-energy-shell processes, specifically virtual processes such as those
relevant for ground-state energy shifts and dispersion van der Waals and
Casimir-Polder interactions, while on-energy-shell processes are excluded.
These effective Hamiltonians allow for a considerable simplification of the
calculation of radiative energy shifts, dispersion, and Casimir-Polder
interactions, including in the presence of boundary conditions. They can also
provide clear physical insights into the processes involved. We clarify that
the form of the effective Hamiltonian depends on the field states considered,
and consequently different expressions can be obtained, each of them with a
well-defined range of validity and possible applications. We also apply our
results to some specific cases, mainly the Lamb shift, the Casimir-Polder
atom-surface interaction, and the dispersion interactions between atoms,
molecules, or, in general, polarizable bodies.
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