Scale invariance and chiral noninvariance in a four-dimensional interacting field theory

R. Acharya, Z. Horváth

Research output: Article

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 languageEnglish
Pages (from-to)47-63
Number of pages17
JournalIl Nuovo Cimento A Series 11
Volume33
Issue number1
DOIs
Publication statusPublished - máj. 1976

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invariance
quarks
quark models
gluons
quantum electrodynamics
substructures
electrodynamics
hadrons
counters
sectors
bosons
theorems
wave functions
propagation
cross sections

ASJC Scopus subject areas

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

Cite this

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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 Kall{\'e}n's conjecture in quantum electrodynamics and c) a counter-example to the extension of the Federbush-Johnson-Jost-Schr{\"o}er theorem outside the charge-zero sector of the present model.",
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