Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model

Abstract

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory to order 1/N in the 2PI-1/N expansion. We show that the renormalization of the broken-symmetry theory depends only on the counter terms of the symmetric theory with $\varphi =0$. We find that the 2PI-1/N expansion violates the Goldstone theorem at order 1/N. In using the O(4) model as a low energy effective field theory of pions to study the time evolution of disoriented chiral condensates one has to {\em{explicitly}} break the O(4) symmetry to give the physical pions a nonzero mass. In this effective theory the {\em additional} small contribution to the pion mass due to the violation of the Goldstone theorem in the 2-PI-1/N equations should be numerically unimportant.

References in corpus (2)

• Tachyonic preheating using 2PI-1/N dynamics and the classical approximation
• Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory

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