### Abstract

The quantum-electrodynamical S matrix is obtained as the set of on-mass-shell values of the renormalized momentum-space Green's functions multiplied by Ci(mi2-pi2)1+i for each particle i, where i is proportional to the fine-structure constant and Ci is a constant. A photon mass is not needed to eliminate virtual infrared divergences. Instead the parameters i=mi2-pi2 regularize Feynman integrals in the infrared region, and the dependence on the i is canceled against the expansion of (mi2-pi2)i multiplying lower-order Green's functions. Exact cross-section formulas are developed which express transition rates in terms of this S matrix. They account for radiation damping nonperturbatively, whereas the S matrix must be calculated perturbatively as a power series in. It is seen that in processes with very small energy loss to unobserved photons individual elements of the quantum-electrodynamical S matrix are directly observable. Rules for practical calculations are summarized.

Original language | English (US) |
---|---|

Pages (from-to) | 3504-3530 |

Number of pages | 27 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 11 |

Issue number | 12 |

DOIs | |

State | Published - 1975 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

**Scattering theory for quantum electrodynamics. II. Reduction and cross-section formulas.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 11, no. 12, pp. 3504-3530. https://doi.org/10.1103/PhysRevD.11.3504

}

TY - JOUR

T1 - Scattering theory for quantum electrodynamics. II. Reduction and cross-section formulas

AU - Zwanziger, Daniel

PY - 1975

Y1 - 1975

N2 - The quantum-electrodynamical S matrix is obtained as the set of on-mass-shell values of the renormalized momentum-space Green's functions multiplied by Ci(mi2-pi2)1+i for each particle i, where i is proportional to the fine-structure constant and Ci is a constant. A photon mass is not needed to eliminate virtual infrared divergences. Instead the parameters i=mi2-pi2 regularize Feynman integrals in the infrared region, and the dependence on the i is canceled against the expansion of (mi2-pi2)i multiplying lower-order Green's functions. Exact cross-section formulas are developed which express transition rates in terms of this S matrix. They account for radiation damping nonperturbatively, whereas the S matrix must be calculated perturbatively as a power series in. It is seen that in processes with very small energy loss to unobserved photons individual elements of the quantum-electrodynamical S matrix are directly observable. Rules for practical calculations are summarized.

AB - The quantum-electrodynamical S matrix is obtained as the set of on-mass-shell values of the renormalized momentum-space Green's functions multiplied by Ci(mi2-pi2)1+i for each particle i, where i is proportional to the fine-structure constant and Ci is a constant. A photon mass is not needed to eliminate virtual infrared divergences. Instead the parameters i=mi2-pi2 regularize Feynman integrals in the infrared region, and the dependence on the i is canceled against the expansion of (mi2-pi2)i multiplying lower-order Green's functions. Exact cross-section formulas are developed which express transition rates in terms of this S matrix. They account for radiation damping nonperturbatively, whereas the S matrix must be calculated perturbatively as a power series in. It is seen that in processes with very small energy loss to unobserved photons individual elements of the quantum-electrodynamical S matrix are directly observable. Rules for practical calculations are summarized.

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U2 - 10.1103/PhysRevD.11.3504

DO - 10.1103/PhysRevD.11.3504

M3 - Article

VL - 11

SP - 3504

EP - 3530

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -