### Abstract

The purpose of this paper is twofold. First, we compare, in detail, the derivation of the Casimir-Polder interaction using time-ordered perturbation theory, to the matching of the scattering amplitude using quantum electrodynamics. In the first case, a total of twelve time-ordered diagrams need to be considered, while in the second case, one encounters only two Feynman diagrams, namely, the ladder and crossed-ladder contributions. For ground-state interactions, we match the contribution of six of the time-ordered diagrams against the corresponding Feynman diagrams, showing the consistency of the two approaches. Second, we also examine the leading radiative correction to the long-range interaction, which is of relative order O(α^{3}). In doing so, we uncover logarithmic terms, in both the interatomic distance as well as the fine-structure constant, in higher-order corrections to the Casimir-Polder interaction.

Original language | English |
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Article number | 215002 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 51 |

Issue number | 21 |

DOIs | |

Publication status | Published - Oct 16 2018 |

### Keywords

- Casimir-Polder interactions
- covariant formalism
- propagator denominator
- radiative corrections
- scattering matrix
- time-ordered perturbation theory

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics