### Abstract

We study the model which results from quantum electrodynamics if all photons are replaced by their longitudinal parts -k1/4 k1/4(k2)2. The model is formulated in terms of a Lagrangian which features the higher-order or "grandfather" potential S which becomes a local field after quantization and from which the vector potential is derived by A1/4=S. The grandfather potential provides a convenient control over ultraviolet and infrared divergences, for its free propagator -(12)i(k1/4)[k1/4ln(-a2k2-iu)(-k2-iu)2] already contains the parameter a-1 with dimensions of mass which otherwise only appears in the theory, after regularization, as a renormalization mass. It produces much needed states, for we prove that there is no charged state satisfying the Gupta-Bleuler condition in DFO(A,), the closure of the space obtained from the vacuum by applying polynomials in A and (the charged spinor field), but such states are easily found in D(S,). As the lesson from the model, a new Lagrangian for quantum electrodynamics is exhibited, which features the grandfather or Hertz potential 1/41/2=- 1/21/4, from which the vector potential is derived by A1/4=1/4 1/2 1/3, and which is expected to yield corresponding advantages.

Original language | English (US) |
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Pages (from-to) | 457-468 |

Number of pages | 12 |

Journal | Physical Review D |

Volume | 17 |

Issue number | 2 |

DOIs | |

State | Published - 1978 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D*,

*17*(2), 457-468. https://doi.org/10.1103/PhysRevD.17.457