Bound-state effective potential formulation of dynamical symmetry breaking
- 15 August 1977
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 16 (4), 1211-1220
- https://doi.org/10.1103/physrevd.16.1211
Abstract
We propose an approximation procedure for studying dynamical symmetry breaking that closely parallels scalar field models of spontaneous symmetry breaking. We focus our attention on the role a deep scalar bound state plays in effecting a phase transition. We show that a viable approximation to the effective potential must contain all one-particle-reducible bound-state pole structures. This dictates a Dyson equation for the self-energy even in the simplest approximation. For theories with 4-field interactions this can reduce to a closed-form Hartree approximation. We look at trilinear interactions where the Dyson integral equation is intractible because of its nonlinearity. Without linearizing the Dyson equation we extract a bound-state contribution to the effective potential. We end up with a generalized effective potential that is a function of classical fields representing the bound state. We show that this contribution displays the proper phase transition when the theory becomes unstable due to a composite tachyon.Keywords
This publication has 16 references indexed in Scilit:
- Bound states, tachyons, and restoration of symmetry in theexpansionPhysical Review D, 1976
- Dynamical symmetry breaking via a bound state and a comment on theO(N) σmodelPhysical Review D, 1976
- Quantum fluctuations in afield theory. I. Stability of the vacuumPhysical Review D, 1975
- Bound states and the effective potential in field theoriesPhysical Review D, 1975
- Asymptotic freedom and Goldstone realization of chiral symmetryPhysical Review D, 1974
- Nonperturbative effective potential fortheory in the many-field limitPhysical Review D, 1974
- Goldstone Bosons as Bound States in the Quark-Gluon ModelPhysical Review D, 1973
- Gauge Invariance and Mass. IIPhysical Review B, 1962
- Gauge Invariance and MassPhysical Review B, 1962
- Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. IPhysical Review B, 1961