CONSTRUCTION OF QUANTIZED GAUGE FIELDS .1. GENERAL RESULTS

In this paper gauge theories are analyzed from the point of view of constructive quantum field theory. Diamagnetic inequalities for general lattice gauge theories are proven. They say that in a local field theory the ground-state energy density rises when the fields (scalars, Dirac fields, etc.) are minimally coupled to an external gauge field. A mass generation mechanism is described. Abelian Higgs models (scalar QED) on the lattice are investigated in more detail: Strong diamagnetic inequalities; infrared bounds; correlation inequalities yielding monotonicity in the space-time cutoff, in the mass of the photon and in the electric charge; gauge invariance and Osterwalder-Schrader positivity,etc., are shown to hold uniformly in the lattice spacing. For the two-dimensional Higgs model on the lattice the θ-vacua are constructed, a first-order phase transition at θ = π and the confinement of fractionally charged quarks are described. Details and applications to the two-dimensional Higgs model in the continuum limit appear in subsequent papers. © 1979.