Ondelettes: The spinor QED3 connection
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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. 1990.
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