Improved effective-potential formalism for composite fields

We develop an effective-potential formalism for studying dynamical symmetry breaking. The potential that we calculate is single-valued and bounded from below. Our formalism incorporates a stability criterion for deciding whether the broken-symmetry solution to the theory is the physical one. In lowest-order calculations in gauge theories we find that the asymmetric theory will be stable if and only if a composite Goldstone boson can be bound. Our conclusion is that in the weak-coupling approximation there is no dynamical spontaneous breakdown in gauge theories. We then use the renormalization group to argue that if spontaneous breakdown occurs at all, it must also occur for arbitrarily weak coupling. The renormalization group also provides us with evidence that dynamical symmetry breakdown does not occur in infrared-stable theories.