Ondelettes: The spinor QED3 connection

Abstract

It is known that the formal perturbation theory of spinor quantum electrodynamics in three space-time dimensions requires no ultraviolet renormalization. We introduce an ondelette cluster expansion (with an infrared cutoff) which converges without counter-terms for weak coupling, thus making the knowledge rigorous. Following the formalism of Lesniewski, we integrate out the bosons at the outset to make the genuine absence of a large-field problem transparent. The combinatoric part of the convergence proof—indeed the precise case-by-case definition of the inductive expansion—is reserved for a subsequent paper. In this paper we publicize the language of ondelette diagrams—originally introduced by Federbush—and describe the correspondence to Feynman diagrams.