Convergence Theorem for Non-commutative Feynman Graphs and Renormalization

Abstract

We present a rigorous proof of the convergence theorem for the Feynman graphs in arbitrary massive Euclidean quantum field theories on non-commutative R^d (NQFT). We give a detailed classification of divergent graphs in some massive NQFT and demonstrate the renormalizability of some of these theories.Comment: Latex, 71 pages, many postscript figures; v2: Comments on massless case added/corrected in sec.8, refs. adde