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In this paper we study the renormalization of the Schwinger-Dyson equationsthat arise in the auxiliary field formulation of the O(N) $\phi^4$ fieldtheory. The auxiliary field formulation allows a simple interpretation of thelarge-N expansion as a loop expansion of the generating functional in theauxiliary field $\chi$, once the effective action is obtained by integratingover the $\phi$ fields. Our all orders result is then used to obtain finiterenormalized Schwinger-Dyson equations based on truncation expansions whichutilize the two-particle irreducible (2-PI) generating function formalism. Wefirst do an all orders renormalization of the two- and three-point functionequations in the vacuum sector. This result is then used to obtain explicitlyfinite and renormalization constant independent self-consistent S-D equationsvalid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results forthe real and imaginary parts of the renormalized Green's functions with therelated \emph{sunset} approximation to the 2-PI equations discussed by Van Heesand Knoll, and comment on the importance of the Landau pole effect.Comment: 20 pages, 10 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>field theory

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation ofλϕ4field theory