Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $λϕ^4$ field theory

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dc.creatorCooper, Fred
dc.creatorMihaila, Bogdan
dc.creatorDawson, John F.
dc.date2004-07-09
dc.date2004-08-24
dc.date.accessioned2026-07-07T11:31:38Z
dc.date.available2026-07-07T11:31:38Z
dc.descriptionIn this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) $ϕ^4$ field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field $χ$, once the effective action is obtained by integrating over the $ϕ$ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent S-D equations valid to order~1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green's functions with the related \emph{sunset} approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.
dc.description20 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/hep-ph/0407119
dc.identifierhttp://arxiv.org/abs/hep-ph/0407119
dc.identifierPhys.Rev.D70:105008,2004
dc.identifierdoi:10.1103/PhysRevD.70.105008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/197330
dc.subjectHigh Energy Physics - Phenomenology
dc.titleRenormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $λϕ^4$ field theory
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