Covariant Gaussian approximation. II. Scalar theories

Journal Article · Sat Jul 15 04:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.40.504· OSTI ID:5873845

Rosenstein, B; Kovner, A

We apply the covariant Gaussian approximation to the one- and/ital N/-component /phi//sup 4/ scalar theories in 3+1dimensions. The diagrammatic representation of the approximation is obtainedand its connection with perturbation theory is discussed. Green's functions atnonzero momenta are calculated and the full renormalization program issystematically carried through. It is found that the only solution ofnormalization conditions is the ''precarious'' theory with infinitesimalnegative bare coupling. The theory with positive bare coupling is trivial. Inthe precarious theory the symmetric (/phi/=0) phase and asymmetric(/phi//ne/0) phase are found. The symmetric phase has always lower energyand there is no spontaneous symmetry breaking in the Gaussian approximation.

• Research Organization: Theory Group, Department of Physics, University of Texas, Austin, Texas 78712(US); High Energy Physics Department, School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
• OSTI ID: 5873845
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 40:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONS
GAUSSIAN PROCESSES
GREEN FUNCTION
HAMILTONIANS
LAGRANGIAN FUNCTION
MATHEMATICAL OPERATORS
PERTURBATION THEORY
PHI4-FIELD THEORY
PROPAGATOR
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RENORMALIZATION
SCALAR FIELDS
SYMMETRY BREAKING