Renormalization of the broken-symmetry two-dimensional SU(N) sigma model and (psi-barpsi)/sup 2/ model

Journal Article · Sat Dec 15 00:00:00 EST 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.3336· OSTI ID:5729011

Cooper, F; Guralnik, G; Haymaker, R W; Tamvakis, K

We derive the renormalized Schwinger-Dyson equations for the two-dimensional SU(N) sigma model with N psi/sub i/ and one sigma and the (psi-bar/sup i/psi/sup i/)/sup 2/ model with spontaneously broken symmetry not = 0. We study the sigma model in the composite limit when the sigma wave-function renormalization constant Z/sub 3/ and the 4-sigma vertex renormalization constant Z/sub 4/ are zero and find that the renormalized Green's functions of the sigma model become identical to those of the (psi-barpsi)/sup 2/ model. In the composite limit of the sigma model the renormalized coupling constants gpsi-barpsisigma and lambda/sub 4sigma/ are related and become calculable in terms of the spontaneously generated fermion mass. We obtain the renormalized gap equation for M/sub sigma/ /sup 2/ which determines the minimum of the effective potential and discuss the Callan-Symanzik equations for the broken-symmetry sector of these models. We show that the Z/sub 3/=Z/sub 4/=0 limit of the sigma model is obtained at the fixed point ..beta..=0 of the Callan-Symanzik equations.

• Research Organization: Theoretical Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87545
• OSTI ID: 5729011
• Journal Information: Phys. Rev., D; (United States), Vol. 20:12
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DYSON REPRESENTATION
RENORMALIZATION
SIGMA MODEL
SU GROUPS
SYMMETRY BREAKING
COUPLING CONSTANTS
EQUATIONS OF MOTION
GAUGE INVARIANCE
GREEN FUNCTION
HIGGS BOSONS
PERTURBATION THEORY
PROPAGATOR
PSI RESONANCES
VERTEX FUNCTIONS
WAVE FUNCTIONS
BOSONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FUNCTIONS
HADRONS
INTERMEDIATE BOSONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MESON RESONANCES
MESONS
PARTICLE MODELS
POSTULATED PARTICLES
RESONANCE PARTICLES
SYMMETRY GROUPS
VECTOR MESONS
645201* - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
645400 - High Energy Physics- Field Theory