### Abstract

A variant of the « finite » field theory approach of Gell-Mann and Low is presented in a massless quark model with singlet gluons. A solution is exhibited for which the gluon wave function renormalization constant is finite but with the quark bare mass infinite. Its spacetime structure is very different from the zero-physical-mass limit of the Adler-Baker-Johnson-Willey electrodynamics. The quark propagator exhibits a square-root cut running from p^{ 2} = 0 to ∞ and it breaks γ_{ 5}-invariance but yet preserves scale invariance. The quark-gluon substructure remains unobservable. An interesting consequence of the model is the departure of the e^{+}e^{-} annihilation cross-section into hadrons from the free-quark model result. The other features are a) the existence of Goldstone bosons, b) an explicit realization of Kallén's conjecture in quantum electrodynamics and c) a counter-example to the extension of the Federbush-Johnson-Jost-Schröer theorem outside the charge-zero sector of the present model.

Original language | English |
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Pages (from-to) | 47-63 |

Number of pages | 17 |

Journal | Il Nuovo Cimento A Series 11 |

Volume | 33 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 1 1976 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics