2004/07/31 by Fred Cooper, Bogdan Mihaila, John F. Dawson · 6 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #hep-ph
paper · pdf · doi:10.1103/physrevd.70.105008
published as Phys.Rev.D70:105008,2004 · 20 pages, 10 figures
arxiv created 2004/08/24 · openalex publication_date 2004/11/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) \ensuremathφ4 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 \ensuremathχ, once the effective action is obtained by integrating over the \ensuremathφ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson (SD) 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 SD 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 sunset approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.