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

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 fromp2 = 0 to ∞ and it breaksγ5-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 area) the existence of Goldstone bosons,b) an explicit realization of Kallen’s conjecture in quantum electrodynamics andc) a counter-example to the extension of the Federbush-Johnson-Jost-Schroer theorem outside the charge-zero sector of the present model.