Bound-state effective potential formulation of dynamical symmetry breaking

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.