Collapse of the wave function, anomalous dimensions and continuum limits in model scalar field theories

Abstract

We study a model scalar field theory with vector couplings in the ladder approximation. A massless bound state appears in the spectrum when the coupling exceeds a critical value αc∼1. The physical mechanism behind this critical point is “collapse of the wave function”, the same as for quenched spinor QED. Composite operators acquire large, negative anomalous dimensions and φ8 interactions become renormalizable above the critical coupling.