### Abstract

A weak asymptotic limit is proposed for a charged field as an operator on the space of asymptotic states. This leads to a modified Lehmann-Symanzik-Zimmermann reduction formula and a determination of the singularity near the mass shell of the Green's function of a charged particle in the presence of other charged particles. Coherent states of the electromagnetic field are also reduced out. The resultant expression for S-matrix elements in terms of vacuum expectation values of time-ordered fields yields a slight elaboration of the Feynman rules which allows a perturbative calculation that is free of infrared and Coulombic divergences order by order. As an application, the amplitude for scattering of a Dirac particle by an external Coulomb potential is calculated to second order in the external potential, with a finite result.

Original language | English (US) |
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Pages (from-to) | 1082-1099 |

Number of pages | 18 |

Journal | Physical Review D |

Volume | 7 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1973 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*7*(4), 1082-1099. https://doi.org/10.1103/PhysRevD.7.1082