Renormalized broken-symmetry Schwinger-Dyson equations and the two-particle irreducible 1/N expansion for the O(N) model

Journal Article · Sun May 01 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.096003· OSTI ID:20709410

Cooper, Fred; Dawson, John F; Mihaila, Bogdan ^[1]

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1. National Science Foundation, Division of Physics, Arlington, Virginia 22230 (United States)

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of Coleman, Jackiw, and Politzer [S. Coleman, R. Jackiw, and H. D. Politzer, Phys. Rev. D 10, 2491 (1974).] for {lambda}{phi}{sup 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 {phi}=0, as discussed in our previous paper [F. Cooper, B. Mihaila, and J. F.Dawson, Phys. Rev. D 70, 105008 (2004).]. 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 explicitly break the O(4) symmetry to give the physical pions a nonzero mass. In this effective theory, we expect that the additional small contribution to the pion mass due to the violation of the Goldstone theorem in the 2PI-1/N equations to be unimportant for an adequate description of the phenomenology.

• OSTI ID: 20709410
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRALITY
O GROUPS
PHI4-FIELD THEORY
PIONS
RENORMALIZATION
REST MASS
SCHWINGER FUNCTIONAL EQUATIONS
SYMMETRY
SYMMETRY BREAKING