Dynamical Vacuum Research Articles

On the dynamical vacuum rearrangement and the problem of fermion mass generation

We discuss the conditions under which the dynamical fermion mass generation mechanism may occur. The analogy between the vacuum rearrangement in massless electrodynamics, which results in the generation of a physical fermion mass, and the vacuum rearrangement concerned with the fall into the Coulomb centre with a large charge ( Z > 137) is considered.

Dynamical symmetry breaking as a bootstrap

This paper is concerned with the bootstrap nature of dynamical symmetry breaking and with the infrared origins of the mass of the electron. We present a general calculational procedure for handling the situation in which a composite operator $\overline{\ensuremath{\Psi}}\ensuremath{\Psi}$ acquires a dynamical vacuum expectation value. We apply our procedure to finite quantum electrodynamics to show how the infrared divergences of the theory self-consistently cause $〈\overline{\ensuremath{\Psi}}\ensuremath{\Psi}〉$ to become nonzero nonperturbatively so that it can provide a scale for a purely dynamical electron mass. Since no Goldstone boson need accompany this spontaneous breakdown, the electron mass bootstraps itself about the ${\ensuremath{\gamma}}_{5}$ degenerate vacuum. The mechanism also yields a new eigenvalue condition for the fine-structure constant. We discuss the deep interplay between the ultraviolet and the infrared, a characteristic feature of dynamical symmetry breaking. We use this interplay to show how to extend the Wilson operator-product expansion to the situation in which there is a degenerate vacuum. We discuss the possibility that the infrared structure of the weak interaction provides a dynamical origin for the Gell-Mann, Oakes, and Renner Hamiltonian. We indicate briefly the possibility that anomalous dimensions can soften a 4-Fermi interaction sufficiently to make it renormalizable.